Riemann zeta function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Riemann zeta function" in English language version.

refsWebsite

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30doi.org

2^nd place

18arxiv.org

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9semanticscholar.org

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7ams.org

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6harvard.edu

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4web.archive.org

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3oeis.org

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2worldcat.org

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1digizeitschriften.de

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1colgate.edu

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ams.org (Global: 451^st place; English: 277^th place)

mathscinet.ams.org

Mollin, Richard A. (2010). Advanced Number Theory with Applications. Discrete Mathematics and its Applications (Boca Raton). CRC Press, Boca Raton, FL. p. 220. ISBN 978-1-4200-8328-6. MR 2560324.
Conrey, J. B. (1989). "More than two fifths of the zeros of the Riemann zeta function are on the critical line". J. Reine Angew. Math. 1989 (399): 1–26. doi:10.1515/crll.1989.399.1. MR 1004130. S2CID 115910600.
Diamond, Harold G. (1982). "Elementary methods in the study of the distribution of prime numbers". Bulletin of the American Mathematical Society. 7 (3): 553–589. doi:10.1090/S0273-0979-1982-15057-1. MR 0670132.
Hashimoto, Yasufumi; Iijima, Yasuyuki; Kurokawa, Nobushige; Wakayama, Masato (2004). "Euler's constants for the Selberg and the Dedekind zeta functions". Bulletin of the Belgian Mathematical Society, Simon Stevin. 11 (4): 493–516. doi:10.36045/bbms/1102689119. MR 2115723.
Odlyzko, A. M.; Schönhage, A. (1988). "Fast algorithms for multiple evaluations of the Riemann zeta function". Trans. Amer. Math. Soc. 309 (2): 797–809. doi:10.2307/2000939. JSTOR 2000939. MR 0961614.

ams.org

Sondow, Jonathan (1994). "Analytic continuation of Riemann's zeta function and values at negative integers via Euler's transformation of series" (PDF). Proceedings of the American Mathematical Society. 120 (2): 421–424. doi:10.1090/S0002-9939-1994-1172954-7.
Biane, Philippe; Pitman, Jim; Yor, Marc (2001). "Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions". Bulletin of the American Mathematical Society. New Series. 38 (4). American Mathematical Society: 435–465. doi:10.1090/S0273-0979-01-00912-0. Retrieved 27 July 2025.

archive.org (Global: 6^th place; English: 6^th place)

Knopp, Konrad (1947). Theory of Functions, Part Two. New York, Dover publications. pp. 51–55.

arxiv.org (Global: 69^th place; English: 59^th place)

Steuding, Jörn; Suriajaya, Ade Irma (1 November 2020). "Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines". Computational Methods and Function Theory. 20 (3): 389–401. arXiv:2007.14661. doi:10.1007/s40315-020-00316-x. hdl:2324/4483207. ISSN 2195-3724. S2CID 216323223. Theorem 2 implies that ζ has an essential singularity at infinity
Pratt, Kyle; Robles, Nicolas; Zaharescu, Alexandru; Zeindler, Dirk (2020). "More than five-twelfths of the zeros of $\zeta$ are on the critical line". Research in the Mathematical Sciences. 7. arXiv:1802.10521. doi:10.1007/s40687-019-0199-8.
Trudgian, Timothy S. (2014). "An improved upper bound for the argument of the Riemann zeta function on the critical line II". J. Number Theory. 134: 280–292. arXiv:1208.5846. doi:10.1016/j.jnt.2013.07.017.
Platt, David; Trudgian, Timothy S. (2021). "The Riemann hypothesis is true up to 3⋅10¹²". Bulletin of the London Mathematical Society. 53 (3): 792–797. arXiv:2004.09765. doi:10.1112/blms.12460.
Mossinghoff, Michael J.; Trudgian, Timothy S.; Yang, Andrew (2024). "Explicit zero-free regions for the Riemann zeta-function". Res. Number Theory. 10 11. arXiv:2212.06867. doi:10.1007/s40993-023-00498-y.
Mossinghoff, Michael J.; Trudgian, Timothy S. (2015). "Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function". J. Number Theory. 157: 329–349. arXiv:1410.3926. doi:10.1016/J.JNT.2015.05.010. S2CID 117968965.
Yang, Andrew (2024). "Explicit bounds on $\zeta (s)$ in the critical strip and a zero-free region". J. Math. Anal. Appl. 534 (2) 128124. arXiv:2301.03165. doi:10.1016/j.jmaa.2024.128124.
Bellotti, Chiara (2024). "Explicit bounds for the Riemann zeta function and a new zero-free region". J. Math. Anal. Appl. 536 (2) 128249. arXiv:2306.10680. doi:10.1016/j.jmaa.2024.128249.
Ford, K. (2002). "Vinogradov's integral and bounds for the Riemann zeta function". Proc. London Math. Soc. 85 (3): 565–633. arXiv:1910.08209. doi:10.1112/S0024611502013655. S2CID 121144007.
Steuding, Jörn (2007). Value-Distribution of L-Functions. Lecture Notes in Mathematics. Vol. 1877. Berlin: Springer. p. 19. arXiv:1711.06671. doi:10.1007/978-3-540-44822-8. ISBN 978-3-540-26526-9.
Blagouchine, Iaroslav V. (2018). "Three Notes on Ser's and Hasse's Representations for the Zeta-functions". INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A: 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.
Blagouchine, Iaroslav V. (2016). "Expansions of generalized Euler's constants into the series of polynomials in $π$ ⁻² and into the formal enveloping series with rational coefficients only". Journal of Number Theory. 158: 365–396. arXiv:1501.00740. doi:10.1016/j.jnt.2015.06.012.
Báez-Duarte, Luis (2010). "On Maslanka's Representation for the Riemann Zeta Function". International Journal of Mathematics and Mathematical Sciences. 2010: 1–9. arXiv:math/0307214. doi:10.1155/2010/714147.
Flajolet, Philippe; Vepstas, Linas (2008). "On Differences of Zeta Values". Journal of Computational and Applied Mathematics. 220 (1–2 October): 58–73. arXiv:math/0611332. Bibcode:2008JCoAM.220...58F. doi:10.1016/j.cam.2007.07.040.
Maślanka, Krzysztof; Koleżyński, Andrzej (2022). "The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm". Computational Methods in Science and Technology. 28 (2): 47–59. arXiv:2210.04609. doi:10.12921/cmst.2022.0000014. S2CID 252780397.
Báez-Duarte, Luis (2003). "A New Necessary and Sufficient Condition for the Riemann Hypothesis". Number Theory. arXiv:math/0307215. Bibcode:2003math......7215B.
Maślanka, Krzysztof (2006). "Báez-Duarte's Criterion for the Riemann Hypothesis and Rice's Integrals". Number Theory. arXiv:math/0603713v2. Bibcode:2006math......3713M.
Komatsu, Takao; Mező, István (2016). "Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers". Publicationes Mathematicae Debrecen. 88 (3–4): 357–368. arXiv:1510.05799. doi:10.5486/pmd.2016.7361. S2CID 55741906.

books.google.com (Global: 3^rd place; English: 3^rd place)

Mollin, Richard A. (2010). Advanced Number Theory with Applications. Discrete Mathematics and its Applications (Boca Raton). CRC Press, Boca Raton, FL. p. 220. ISBN 978-1-4200-8328-6. MR 2560324.

claymath.org (Global: 8,402^nd place; English: 8,241^st place)

Bombieri, Enrico. "The Riemann Hypothesis – official problem description" (PDF). Clay Mathematics Institute. Archived from the original (PDF) on 22 December 2015. Retrieved 8 August 2014.

colgate.edu (Global: low place; English: 9,382^nd place)

math.colgate.edu

Blagouchine, Iaroslav V. (2018). "Three Notes on Ser's and Hasse's Representations for the Zeta-functions". INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A: 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.

digizeitschriften.de (Global: 5,626^th place; English: 8,880^th place)

Conrey, J. B. (1989). "More than two fifths of the zeros of the Riemann zeta function are on the critical line". J. Reine Angew. Math. 1989 (399): 1–26. doi:10.1515/crll.1989.399.1. MR 1004130. S2CID 115910600.

doi.org (Global: 2^nd place; English: 2^nd place)

Steuding, Jörn; Suriajaya, Ade Irma (1 November 2020). "Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines". Computational Methods and Function Theory. 20 (3): 389–401. arXiv:2007.14661. doi:10.1007/s40315-020-00316-x. hdl:2324/4483207. ISSN 2195-3724. S2CID 216323223. Theorem 2 implies that ζ has an essential singularity at infinity
Conrey, J. B. (1989). "More than two fifths of the zeros of the Riemann zeta function are on the critical line". J. Reine Angew. Math. 1989 (399): 1–26. doi:10.1515/crll.1989.399.1. MR 1004130. S2CID 115910600.
Pratt, Kyle; Robles, Nicolas; Zaharescu, Alexandru; Zeindler, Dirk (2020). "More than five-twelfths of the zeros of $\zeta$ are on the critical line". Research in the Mathematical Sciences. 7. arXiv:1802.10521. doi:10.1007/s40687-019-0199-8.
Trudgian, Timothy S. (2014). "An improved upper bound for the argument of the Riemann zeta function on the critical line II". J. Number Theory. 134: 280–292. arXiv:1208.5846. doi:10.1016/j.jnt.2013.07.017.
Hardy, G. H.; Fekete, M.; Littlewood, J. E. (1 September 1921). "The Zeros of Riemann's Zeta-Function on the Critical Line". Journal of the London Mathematical Society. s1-1: 15–19. doi:10.1112/jlms/s1-1.1.15.
Diamond, Harold G. (1982). "Elementary methods in the study of the distribution of prime numbers". Bulletin of the American Mathematical Society. 7 (3): 553–589. doi:10.1090/S0273-0979-1982-15057-1. MR 0670132.
Platt, David; Trudgian, Timothy S. (2021). "The Riemann hypothesis is true up to 3⋅10¹²". Bulletin of the London Mathematical Society. 53 (3): 792–797. arXiv:2004.09765. doi:10.1112/blms.12460.
Mossinghoff, Michael J.; Trudgian, Timothy S.; Yang, Andrew (2024). "Explicit zero-free regions for the Riemann zeta-function". Res. Number Theory. 10 11. arXiv:2212.06867. doi:10.1007/s40993-023-00498-y.
Mossinghoff, Michael J.; Trudgian, Timothy S. (2015). "Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function". J. Number Theory. 157: 329–349. arXiv:1410.3926. doi:10.1016/J.JNT.2015.05.010. S2CID 117968965.
Yang, Andrew (2024). "Explicit bounds on $\zeta (s)$ in the critical strip and a zero-free region". J. Math. Anal. Appl. 534 (2) 128124. arXiv:2301.03165. doi:10.1016/j.jmaa.2024.128124.
Bellotti, Chiara (2024). "Explicit bounds for the Riemann zeta function and a new zero-free region". J. Math. Anal. Appl. 536 (2) 128249. arXiv:2306.10680. doi:10.1016/j.jmaa.2024.128249.
Ford, K. (2002). "Vinogradov's integral and bounds for the Riemann zeta function". Proc. London Math. Soc. 85 (3): 565–633. arXiv:1910.08209. doi:10.1112/S0024611502013655. S2CID 121144007.
Kainz, A. J.; Titulaer, U. M. (1992). "An accurate two-stream moment method for kinetic boundary layer problems of linear kinetic equations". J. Phys. A: Math. Gen. 25 (7): 1855–1874. Bibcode:1992JPhA...25.1855K. doi:10.1088/0305-4470/25/7/026.
Sondow, Jonathan (1998). "An antisymmetric formula for Euler's constant". Mathematics Magazine. 71 (3): 219–220. doi:10.1080/0025570X.1998.11996638. Archived from the original on 4 June 2011. Retrieved 29 May 2006.
Ramūnas Garunkštis; Antanas Laurinčikas; Kohji Matsumoto; Jörn Steuding; Rasa Steuding (2010). "Effective uniform approximation by the Riemann zeta-function". Publicacions Matemàtiques. 54 (1): 209–219. doi:10.5565/PUBLMAT_54110_12. JSTOR 43736941.
Bhaskar Bagchi (1982). "A Joint Universality Theorem for Dirichlet L-Functions". Mathematische Zeitschrift. 181 (3): 319–334. doi:10.1007/bf01161980. ISSN 0025-5874. S2CID 120930513.
Steuding, Jörn (2007). Value-Distribution of L-Functions. Lecture Notes in Mathematics. Vol. 1877. Berlin: Springer. p. 19. arXiv:1711.06671. doi:10.1007/978-3-540-44822-8. ISBN 978-3-540-26526-9.
Karatsuba, A. A. (2004). "Lower bounds for the maximum modulus of the Riemann zeta function on short segments of the critical line". Izv. Ross. Akad. Nauk, Ser. Mat. 68 (8): 99–104. Bibcode:2004IzMat..68.1157K. doi:10.1070/IM2004v068n06ABEH000513. S2CID 250796539.
Hashimoto, Yasufumi; Iijima, Yasuyuki; Kurokawa, Nobushige; Wakayama, Masato (2004). "Euler's constants for the Selberg and the Dedekind zeta functions". Bulletin of the Belgian Mathematical Society, Simon Stevin. 11 (4): 493–516. doi:10.36045/bbms/1102689119. MR 2115723.
Blagouchine, Iaroslav V. (2018). "Three Notes on Ser's and Hasse's Representations for the Zeta-functions". INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A: 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.
Hasse, Helmut (1930). "Ein Summierungsverfahren für die Riemannsche ζ-Reihe" [A summation method for the Riemann ζ series]. Mathematische Zeitschrift (in German). 32 (1): 458–464. doi:10.1007/BF01194645. S2CID 120392534.
Sondow, Jonathan (1994). "Analytic continuation of Riemann's zeta function and values at negative integers via Euler's transformation of series" (PDF). Proceedings of the American Mathematical Society. 120 (2): 421–424. doi:10.1090/S0002-9939-1994-1172954-7.
Blagouchine, Iaroslav V. (2016). "Expansions of generalized Euler's constants into the series of polynomials in $π$ ⁻² and into the formal enveloping series with rational coefficients only". Journal of Number Theory. 158: 365–396. arXiv:1501.00740. doi:10.1016/j.jnt.2015.06.012.
Báez-Duarte, Luis (2010). "On Maslanka's Representation for the Riemann Zeta Function". International Journal of Mathematics and Mathematical Sciences. 2010: 1–9. arXiv:math/0307214. doi:10.1155/2010/714147.
Flajolet, Philippe; Vepstas, Linas (2008). "On Differences of Zeta Values". Journal of Computational and Applied Mathematics. 220 (1–2 October): 58–73. arXiv:math/0611332. Bibcode:2008JCoAM.220...58F. doi:10.1016/j.cam.2007.07.040.
Maślanka, Krzysztof; Koleżyński, Andrzej (2022). "The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm". Computational Methods in Science and Technology. 28 (2): 47–59. arXiv:2210.04609. doi:10.12921/cmst.2022.0000014. S2CID 252780397.
Wolf, Marek (2014). "Some remarks on the Báez-Duarte criterion for the Riemann Hypothesis". Computational Methods in Science and Technology. 20 (2): 39–47. doi:10.12921/cmst.2014.20.02.39-47.
Komatsu, Takao; Mező, István (2016). "Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers". Publicationes Mathematicae Debrecen. 88 (3–4): 357–368. arXiv:1510.05799. doi:10.5486/pmd.2016.7361. S2CID 55741906.
Biane, Philippe; Pitman, Jim; Yor, Marc (2001). "Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions". Bulletin of the American Mathematical Society. New Series. 38 (4). American Mathematical Society: 435–465. doi:10.1090/S0273-0979-01-00912-0. Retrieved 27 July 2025.
Odlyzko, A. M.; Schönhage, A. (1988). "Fast algorithms for multiple evaluations of the Riemann zeta function". Trans. Amer. Math. Soc. 309 (2): 797–809. doi:10.2307/2000939. JSTOR 2000939. MR 0961614.

earthlink.net (Global: 7,693^rd place; English: 5,406^th place)

home.earthlink.net

Sondow, Jonathan (1998). "An antisymmetric formula for Euler's constant". Mathematics Magazine. 71 (3): 219–220. doi:10.1080/0025570X.1998.11996638. Archived from the original on 4 June 2011. Retrieved 29 May 2006.

ex.ac.uk (Global: low place; English: low place)

empslocal.ex.ac.uk

"Work on spin-chains by A. Knauf, et. al". Empslocal.ex.ac.uk. Retrieved 4 January 2017.

handle.net (Global: 102^nd place; English: 76^th place)

hdl.handle.net

Steuding, Jörn; Suriajaya, Ade Irma (1 November 2020). "Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines". Computational Methods and Function Theory. 20 (3): 389–401. arXiv:2007.14661. doi:10.1007/s40315-020-00316-x. hdl:2324/4483207. ISSN 2195-3724. S2CID 216323223. Theorem 2 implies that ζ has an essential singularity at infinity

harvard.edu (Global: 18^th place; English: 17^th place)

ui.adsabs.harvard.edu

Kainz, A. J.; Titulaer, U. M. (1992). "An accurate two-stream moment method for kinetic boundary layer problems of linear kinetic equations". J. Phys. A: Math. Gen. 25 (7): 1855–1874. Bibcode:1992JPhA...25.1855K. doi:10.1088/0305-4470/25/7/026.
Karatsuba, A. A. (2004). "Lower bounds for the maximum modulus of the Riemann zeta function on short segments of the critical line". Izv. Ross. Akad. Nauk, Ser. Mat. 68 (8): 99–104. Bibcode:2004IzMat..68.1157K. doi:10.1070/IM2004v068n06ABEH000513. S2CID 250796539.
Blagouchine, Iaroslav V. (2018). "Three Notes on Ser's and Hasse's Representations for the Zeta-functions". INTEGERS: The Electronic Journal of Combinatorial Number Theory. 18A: 1–45. arXiv:1606.02044. Bibcode:2016arXiv160602044B. doi:10.5281/zenodo.10581385.
Flajolet, Philippe; Vepstas, Linas (2008). "On Differences of Zeta Values". Journal of Computational and Applied Mathematics. 220 (1–2 October): 58–73. arXiv:math/0611332. Bibcode:2008JCoAM.220...58F. doi:10.1016/j.cam.2007.07.040.
Báez-Duarte, Luis (2003). "A New Necessary and Sufficient Condition for the Riemann Hypothesis". Number Theory. arXiv:math/0307215. Bibcode:2003math......7215B.
Maślanka, Krzysztof (2006). "Báez-Duarte's Criterion for the Riemann Hypothesis and Rice's Integrals". Number Theory. arXiv:math/0603713v2. Bibcode:2006math......3713M.

ipython.org (Global: low place; English: low place)

nbviewer.ipython.org

"Jupyter Notebook Viewer". Nbviewer.ipython.org. Retrieved 4 January 2017.

jstor.org (Global: 26^th place; English: 20^th place)

Ramūnas Garunkštis; Antanas Laurinčikas; Kohji Matsumoto; Jörn Steuding; Rasa Steuding (2010). "Effective uniform approximation by the Riemann zeta-function". Publicacions Matemàtiques. 54 (1): 209–219. doi:10.5565/PUBLMAT_54110_12. JSTOR 43736941.
Odlyzko, A. M.; Schönhage, A. (1988). "Fast algorithms for multiple evaluations of the Riemann zeta function". Trans. Amer. Math. Soc. 309 (2): 797–809. doi:10.2307/2000939. JSTOR 2000939. MR 0961614.

linas.org (Global: low place; English: low place)

"A series representation for the Riemann Zeta derived from the Gauss-Kuzmin-Wirsing Operator" (PDF). Linas.org. Retrieved 4 January 2017.

lmfdb.org (Global: low place; English: low place)

The L-functions and Modular Forms Database. "Zeros of ζ(s)".

oeis.org (Global: 742^nd place; English: 538^th place)

Further digits and references for this constant are available at OEIS: A059750.
"A220335 – OEIS". oeis.org. Retrieved 17 April 2019.
Gene Ward Smith. "Nearest integer to locations of increasingly large peaks of abs(zeta(0.5 + i×2×Pi/log(2)×t)) for increasing real t". The On-Line Encyclopedia of Integer Sequences. Retrieved 4 March 2022.

ox.ac.uk (Global: 613^th place; English: 456^th place)

users.ox.ac.uk

Damm-Johnsenn, Håvard (2019). Theta functions and their applications (PDF). p. 5. Archived from the original (PDF) on 21 March 2025.

projecteuclid.org (Global: 3,707^th place; English: 2,409^th place)

Hashimoto, Yasufumi; Iijima, Yasuyuki; Kurokawa, Nobushige; Wakayama, Masato (2004). "Euler's constants for the Selberg and the Dedekind zeta functions". Bulletin of the Belgian Mathematical Society, Simon Stevin. 11 (4): 493–516. doi:10.36045/bbms/1102689119. MR 2115723.

semanticscholar.org (Global: 11^th place; English: 8^th place)

api.semanticscholar.org

Steuding, Jörn; Suriajaya, Ade Irma (1 November 2020). "Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines". Computational Methods and Function Theory. 20 (3): 389–401. arXiv:2007.14661. doi:10.1007/s40315-020-00316-x. hdl:2324/4483207. ISSN 2195-3724. S2CID 216323223. Theorem 2 implies that ζ has an essential singularity at infinity
Conrey, J. B. (1989). "More than two fifths of the zeros of the Riemann zeta function are on the critical line". J. Reine Angew. Math. 1989 (399): 1–26. doi:10.1515/crll.1989.399.1. MR 1004130. S2CID 115910600.
Mossinghoff, Michael J.; Trudgian, Timothy S. (2015). "Nonnegative trigonometric polynomials and a zero-free region for the Riemann zeta-function". J. Number Theory. 157: 329–349. arXiv:1410.3926. doi:10.1016/J.JNT.2015.05.010. S2CID 117968965.
Ford, K. (2002). "Vinogradov's integral and bounds for the Riemann zeta function". Proc. London Math. Soc. 85 (3): 565–633. arXiv:1910.08209. doi:10.1112/S0024611502013655. S2CID 121144007.
Bhaskar Bagchi (1982). "A Joint Universality Theorem for Dirichlet L-Functions". Mathematische Zeitschrift. 181 (3): 319–334. doi:10.1007/bf01161980. ISSN 0025-5874. S2CID 120930513.
Karatsuba, A. A. (2004). "Lower bounds for the maximum modulus of the Riemann zeta function on short segments of the critical line". Izv. Ross. Akad. Nauk, Ser. Mat. 68 (8): 99–104. Bibcode:2004IzMat..68.1157K. doi:10.1070/IM2004v068n06ABEH000513. S2CID 250796539.
Hasse, Helmut (1930). "Ein Summierungsverfahren für die Riemannsche ζ-Reihe" [A summation method for the Riemann ζ series]. Mathematische Zeitschrift (in German). 32 (1): 458–464. doi:10.1007/BF01194645. S2CID 120392534.
Maślanka, Krzysztof; Koleżyński, Andrzej (2022). "The High Precision Numerical Calculation of Stieltjes Constants. Simple and Fast Algorithm". Computational Methods in Science and Technology. 28 (2): 47–59. arXiv:2210.04609. doi:10.12921/cmst.2022.0000014. S2CID 252780397.
Komatsu, Takao; Mező, István (2016). "Incomplete poly-Bernoulli numbers associated with incomplete Stirling numbers". Publicationes Mathematicae Debrecen. 88 (3–4): 357–368. arXiv:1510.05799. doi:10.5486/pmd.2016.7361. S2CID 55741906.

sfu.ca (Global: 3,413^th place; English: 2,445^th place)

cecm.sfu.ca

Borwein, Peter (2000). "An Efficient Algorithm for the Riemann Zeta Function" (PDF). In Théra, Michel A. (ed.). Constructive, Experimental, and Nonlinear Analysis. Conference Proceedings, Canadian Mathematical Society. Vol. 27. Providence, RI: American Mathematical Society, on behalf of the Canadian Mathematical Society. pp. 29–34. ISBN 978-0-8218-2167-1. Archived from the original (PDF) on 26 July 2011. Retrieved 25 November 2017.

springer.com (Global: 274^th place; English: 309^th place)

link.springer.com

Pratt, Kyle; Robles, Nicolas; Zaharescu, Alexandru; Zeindler, Dirk (2020). "More than five-twelfths of the zeros of $\zeta$ are on the critical line". Research in the Mathematical Sciences. 7. arXiv:1802.10521. doi:10.1007/s40687-019-0199-8.

uab.cat (Global: 6,782^nd place; English: 8,716^th place)

ddd.uab.cat

Ramūnas Garunkštis; Antanas Laurinčikas; Kohji Matsumoto; Jörn Steuding; Rasa Steuding (2010). "Effective uniform approximation by the Riemann zeta-function". Publicacions Matemàtiques. 54 (1): 209–219. doi:10.5565/PUBLMAT_54110_12. JSTOR 43736941.

web.archive.org (Global: 1^st place; English: 1^st place)

Bombieri, Enrico. "The Riemann Hypothesis – official problem description" (PDF). Clay Mathematics Institute. Archived from the original (PDF) on 22 December 2015. Retrieved 8 August 2014.
Damm-Johnsenn, Håvard (2019). Theta functions and their applications (PDF). p. 5. Archived from the original (PDF) on 21 March 2025.
Sondow, Jonathan (1998). "An antisymmetric formula for Euler's constant". Mathematics Magazine. 71 (3): 219–220. doi:10.1080/0025570X.1998.11996638. Archived from the original on 4 June 2011. Retrieved 29 May 2006.
Borwein, Peter (2000). "An Efficient Algorithm for the Riemann Zeta Function" (PDF). In Théra, Michel A. (ed.). Constructive, Experimental, and Nonlinear Analysis. Conference Proceedings, Canadian Mathematical Society. Vol. 27. Providence, RI: American Mathematical Society, on behalf of the Canadian Mathematical Society. pp. 29–34. ISBN 978-0-8218-2167-1. Archived from the original (PDF) on 26 July 2011. Retrieved 25 November 2017.

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Eric Weisstein. "Riemann Zeta Function Zeros". Retrieved 24 April 2021.

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Steuding, Jörn; Suriajaya, Ade Irma (1 November 2020). "Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines". Computational Methods and Function Theory. 20 (3): 389–401. arXiv:2007.14661. doi:10.1007/s40315-020-00316-x. hdl:2324/4483207. ISSN 2195-3724. S2CID 216323223. Theorem 2 implies that ζ has an essential singularity at infinity
Bhaskar Bagchi (1982). "A Joint Universality Theorem for Dirichlet L-Functions". Mathematische Zeitschrift. 181 (3): 319–334. doi:10.1007/bf01161980. ISSN 0025-5874. S2CID 120930513.

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Riemann, Bernhard (1859). "On the number of primes less than a given magnitude". Monatsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin. translated and reprinted in Edwards, H. M. (1974). Riemann's Zeta Function. New York: Academic Press. ISBN 0-12-232750-0. Zbl 0315.10035.

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Hardy, G. H.; Fekete, M.; Littlewood, J. E. (1 September 1921). "The Zeros of Riemann's Zeta-Function on the Critical Line". Journal of the London Mathematical Society. s1-1: 15–19. doi:10.1112/jlms/s1-1.1.15.

Riemann zeta function (English Wikipedia)

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