Fungsi zeta Riemann (Indonesian Wikipedia)
Analysis of information sources in references of the Wikipedia article "Fungsi zeta Riemann" in Indonesian language version.
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ams.org
- 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. Diarsipkan dari versi asli tanggal 2023-07-26. Diakses tanggal 2023-01-25.
- Diamond, Harold G. (1982). "Elementary methods in the study of the distribution of prime numbers". Bulletin of the American Mathematical Society. 7 (3): 553–89. doi:10.1090/S0273-0979-1982-15057-1
. MR 0670132.
archive.org
- Devlin, Keith (2002). The Millennium Problems: The seven greatest unsolved mathematical puzzles of our time. New York: Barnes & Noble. hlm. 43–47. ISBN 978-0-7607-8659-8.
- Ogilvy, C. S.; Anderson, J. T. (1988). Excursions in Number Theory. Dover Publications. hlm. 29–35. ISBN 0-486-25778-9.
arxiv.org
- 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.
- 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.
- 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.
- Steuding, Jörn (2007). Value-Distribution of L-Functions. Lecture Notes in Mathematics. 1877. Berlin: Springer. hlm. 19. arXiv:1711.06671 . doi:10.1007/978-3-540-44822-8. ISBN 978-3-540-26526-9.
centrale-marseille.fr
iblagouchine.perso.centrale-marseille.fr
- Blagouchine, I.V. (1 March 2018). The history of the functional equation of the zeta-function. Seminar on the History of Mathematics. St. Petersburg, RU: Steklov Institute of Mathematics; "online PDF". Diarsipkan dari versi asli tanggal 2018-05-02. Diakses tanggal 2023-01-22.
- Blagouchine, I.V. (2014). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". The Ramanujan Journal. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. Diarsipkan dari versi asli tanggal 2017-12-12. Diakses tanggal 2018-02-01. Blagouchine, I.V. (2017). "Addendum". The Ramanujan Journal. 42: 777–781. doi:10.1007/s11139-015-9763-z. Diarsipkan dari versi asli tanggal 2018-05-02. Diakses tanggal 2023-01-22.
claymath.org
- Bombieri, Enrico. "The Riemann Hypothesis – official problem description" (PDF). Clay Mathematics Institute. Diarsipkan dari versi asli (PDF) tanggal 2015-12-22. Diakses tanggal 2014-08-08.
digizeitschriften.de
- 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. Diarsipkan dari versi asli tanggal 2023-07-26. Diakses tanggal 2023-01-25.
doi.org
- Blagouchine, I.V. (2014). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". The Ramanujan Journal. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. Diarsipkan dari versi asli tanggal 2017-12-12. Diakses tanggal 2018-02-01. Blagouchine, I.V. (2017). "Addendum". The Ramanujan Journal. 42: 777–781. doi:10.1007/s11139-015-9763-z. Diarsipkan dari versi asli tanggal 2018-05-02. Diakses tanggal 2023-01-22.
- 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. Diarsipkan dari versi asli tanggal 2023-07-26. Diakses tanggal 2023-01-25.
- 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. (1921-09-01). "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. Diarsipkan dari versi asli tanggal 2023-02-24. Diakses tanggal 2023-01-25.
- Diamond, Harold G. (1982). "Elementary methods in the study of the distribution of prime numbers". Bulletin of the American Mathematical Society. 7 (3): 553–89. doi:10.1090/S0273-0979-1982-15057-1 . MR 0670132.
- 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.
- 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.
- LeClair, André; França, Guilherme. "Transcendental equations satisfied by the individual zeros of Riemann ζ, Dirichlet and modular L-functions". Communications in number theory and physics. 9 (1): 1–20. doi:10.4310/CNTP.2015.v9.n1.a1.
- 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. Diarsipkan dari versi asli tanggal 2011-06-04. Diakses tanggal 2006-05-29.
- Steuding, Jörn; Suriajaya, Ade Irma (2020-11-01). "Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines". Computational Methods and Function Theory (dalam bahasa Inggris). 20 (3): 389–401. doi:10.1007/s40315-020-00316-x. ISSN 2195-3724. Diarsipkan dari versi asli tanggal 2023-07-26. Diakses tanggal 2023-01-27.
Theorem 2 implies that ζ has an essential singularity at infinity
- 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:10.1090/S0025-5718-1975-0384673-1 . 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.
- Steuding, Jörn (2007). Value-Distribution of L-Functions. Lecture Notes in Mathematics. 1877. Berlin: Springer. hlm. 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.
earthlink.net
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. Diarsipkan dari versi asli tanggal 2011-06-04. Diakses tanggal 2006-05-29.
harvard.edu
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.
ipython.org
nbviewer.ipython.org
- "Jupyter Notebook Viewer". Nbviewer.ipython.org. Diakses tanggal 2017-01-04.
jstor.org
- 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:10.1090/S0025-5718-1975-0384673-1 . JSTOR 43736941.
lmfdb.org
- The L-functions and Modular Forms Database. "Zeros of ζ(s)". Diarsipkan dari versi asli tanggal 2023-07-06. Diakses tanggal 2023-01-25.
mathnet.ru
- Blagouchine, I.V. (1 March 2018). The history of the functional equation of the zeta-function. Seminar on the History of Mathematics. St. Petersburg, RU: Steklov Institute of Mathematics; "online PDF". Diarsipkan dari versi asli tanggal 2018-05-02. Diakses tanggal 2023-01-22.
oeis.org
- Further digits and references for this constant are available at
A059750.
springer.com
link.springer.com
- Blagouchine, I.V. (2014). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". The Ramanujan Journal. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. Diarsipkan dari versi asli tanggal 2017-12-12. Diakses tanggal 2018-02-01. Blagouchine, I.V. (2017). "Addendum". The Ramanujan Journal. 42: 777–781. doi:10.1007/s11139-015-9763-z. Diarsipkan dari versi asli tanggal 2018-05-02. Diakses tanggal 2023-01-22.
web.archive.org
- Bombieri, Enrico. "The Riemann Hypothesis – official problem description" (PDF). Clay Mathematics Institute. Diarsipkan dari versi asli (PDF) tanggal 2015-12-22. Diakses tanggal 2014-08-08.
- Blagouchine, I.V. (1 March 2018). The history of the functional equation of the zeta-function. Seminar on the History of Mathematics. St. Petersburg, RU: Steklov Institute of Mathematics; "online PDF". Diarsipkan dari versi asli tanggal 2018-05-02. Diakses tanggal 2023-01-22.
- Blagouchine, I.V. (2014). "Rediscovery of Malmsten's integrals, their evaluation by contour integration methods and some related results". The Ramanujan Journal. 35 (1): 21–110. doi:10.1007/s11139-013-9528-5. Diarsipkan dari versi asli tanggal 2017-12-12. Diakses tanggal 2018-02-01. Blagouchine, I.V. (2017). "Addendum". The Ramanujan Journal. 42: 777–781. doi:10.1007/s11139-015-9763-z. Diarsipkan dari versi asli tanggal 2018-05-02. Diakses tanggal 2023-01-22.
- 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. Diarsipkan dari versi asli tanggal 2023-07-26. Diakses tanggal 2023-01-25.
- Eric Weisstein. "Riemann Zeta Function Zeros". Diarsipkan dari versi asli tanggal 2023-07-06. Diakses tanggal 2021-04-24.
- The L-functions and Modular Forms Database. "Zeros of ζ(s)". Diarsipkan dari versi asli tanggal 2023-07-06. Diakses tanggal 2023-01-25.
- Hardy, G. H.; Fekete, M.; Littlewood, J. E. (1921-09-01). "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. Diarsipkan dari versi asli tanggal 2023-02-24. Diakses tanggal 2023-01-25.
- Sondow, Jonathan (1998). "An antisymmetric formula for Euler's constant". Mathematics Magazine. 71 (3): 219–220. doi:10.1080/0025570X.1998.11996638. Diarsipkan dari versi asli tanggal 2011-06-04. Diakses tanggal 2006-05-29.
- Steuding, Jörn; Suriajaya, Ade Irma (2020-11-01). "Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines". Computational Methods and Function Theory (dalam bahasa Inggris). 20 (3): 389–401. doi:10.1007/s40315-020-00316-x. ISSN 2195-3724. Diarsipkan dari versi asli tanggal 2023-07-26. Diakses tanggal 2023-01-27.
Theorem 2 implies that ζ has an essential singularity at infinity
wolfram.com
mathworld.wolfram.com
- Eric Weisstein. "Riemann Zeta Function Zeros". Diarsipkan dari versi asli tanggal 2023-07-06. Diakses tanggal 2021-04-24.
worldcat.org
- Steuding, Jörn; Suriajaya, Ade Irma (2020-11-01). "Value-Distribution of the Riemann Zeta-Function Along Its Julia Lines". Computational Methods and Function Theory (dalam bahasa Inggris). 20 (3): 389–401. doi:10.1007/s40315-020-00316-x. ISSN 2195-3724. Diarsipkan dari versi asli tanggal 2023-07-26. Diakses tanggal 2023-01-27.
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.
zenodo.org
- Hardy, G. H.; Fekete, M.; Littlewood, J. E. (1921-09-01). "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. Diarsipkan dari versi asli tanggal 2023-02-24. Diakses tanggal 2023-01-25.