Lindelöf hypothesis (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Lindelöf hypothesis" in English language version.

refsWebsite

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22doi.org

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18worldcat.org

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9arxiv.org

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6ams.org

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5semanticscholar.org

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2eudml.org

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2harvard.edu

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2psu.edu

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2ias.edu

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2quantamagazine.org

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1biodiversitylibrary.org

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1encyclopediaofmath.org

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1princeton.edu

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aimath.org

"25a". aimath.org. Retrieved 2024-07-16.

ams.org

mathscinet.ams.org

Huxley (2002), Huxley (2005) Huxley, M. N. (2002), "Integer points, exponential sums and the Riemann zeta function", Number theory for the millennium, II (Urbana, IL, 2000), A K Peters, pp. 275–290, MR 1956254 Huxley, M. N. (2005), "Exponential sums and the Riemann zeta function. V", Proceedings of the London Mathematical Society, Third Series, 90 (1): 1–41, doi:10.1112/S0024611504014959, ISSN 0024-6115, MR 2107036
Bourgain (2017) Bourgain, Jean (2017), "Decoupling, exponential sums and the Riemann zeta function", Journal of the American Mathematical Society, 30 (1): 205–224, arXiv:1408.5794, doi:10.1090/jams/860, MR 3556291, S2CID 118064221
Bourgain (2017) Bourgain, Jean (2017), "Decoupling, exponential sums and the Riemann zeta function", Journal of the American Mathematical Society, 30 (1): 205–224, arXiv:1408.5794, doi:10.1090/jams/860, MR 3556291, S2CID 118064221
Heath-Brown (1979) Heath-Brown, D. R. (1979), "The fourth power moment of the Riemann zeta function", Proceedings of the London Mathematical Society, Third Series, 38 (3): 385–422, doi:10.1112/plms/s3-38.3.385, ISSN 0024-6115, MR 0532980
Conrey & Ghosh (1998) Conrey, J. B.; Ghosh, A. (1998), "A conjecture for the sixth power moment of the Riemann zeta-function", International Mathematics Research Notices, 1998 (15): 775–780, arXiv:math/9807187, Bibcode:1998math......7187C, doi:10.1155/S1073792898000476, ISSN 1073-7928, MR 1639551
Keating & Snaith (2000) Keating, Jonathan P.; Snaith, N. C. (2000), "Random matrix theory and ζ(1/2+it)", Communications in Mathematical Physics, 214 (1): 57–89, Bibcode:2000CMaPh.214...57K, CiteSeerX 10.1.1.15.8362, doi:10.1007/s002200000261, ISSN 0010-3616, MR 1794265, S2CID 11095649

arxiv.org

Bourgain (2017) Bourgain, Jean (2017), "Decoupling, exponential sums and the Riemann zeta function", Journal of the American Mathematical Society, 30 (1): 205–224, arXiv:1408.5794, doi:10.1090/jams/860, MR 3556291, S2CID 118064221
Bourgain (2017) Bourgain, Jean (2017), "Decoupling, exponential sums and the Riemann zeta function", Journal of the American Mathematical Society, 30 (1): 205–224, arXiv:1408.5794, doi:10.1090/jams/860, MR 3556291, S2CID 118064221
Conrey & Ghosh (1998) Conrey, J. B.; Ghosh, A. (1998), "A conjecture for the sixth power moment of the Riemann zeta-function", International Mathematics Research Notices, 1998 (15): 775–780, arXiv:math/9807187, Bibcode:1998math......7187C, doi:10.1155/S1073792898000476, ISSN 1073-7928, MR 1639551
Banks, William; Ford, Kevin; Tao, Terence (2023). "Large prime gaps and probabilistic models". Inventiones Mathematicae. 233 (3): 1471–1518. arXiv:1908.08613. doi:10.1007/s00222-023-01199-0. ISSN 0020-9910.
Trudgian, Timothy S.; Yang, Andrew (2023). "Toward optimal exponent pairs". arXiv:2306.05599 [math.NT].
Guth, Larry; Maynard, James (2024). "New large value estimates for Dirichlet polynomials". arXiv:2405.20552 [math.NT].
Bernstein, Joseph; Reznikov, Andre (2010-10-05). "Subconvexity bounds for triple L -functions and representation theory". Annals of Mathematics. 172 (3): 1679–1718. arXiv:math/0608555. doi:10.4007/annals.2010.172.1679. ISSN 0003-486X. S2CID 14745024.
Michel, Philippe; Venkatesh, Akshay (2010). "The subconvexity problem for GL₂". Publications Mathématiques de l'IHÉS. 111 (1): 171–271. arXiv:0903.3591. CiteSeerX 10.1.1.750.8950. doi:10.1007/s10240-010-0025-8. S2CID 14155294.
Nelson, Paul D. (2021-09-30). "Bounds for standard $L$-functions". arXiv:2109.15230 [math.NT].

biodiversitylibrary.org

Backlund (1918–1919) Backlund, R. (1918–1919), "Über die Beziehung zwischen Anwachsen und Nullstellen der Zeta-Funktion", Ofversigt Finska Vetensk. Soc., 61 (9)

doi.org

Hardy, G. H.; Littlewood, J. E. (1916). "Contributions to the theory of the riemann zeta-function and the theory of the distribution of primes". Acta Mathematica. 41: 119–196. doi:10.1007/BF02422942. ISSN 0001-5962.
Titchmarsh, E. C. (1932). "On van der Corput's method and the zeta-function of Riemann (III)". The Quarterly Journal of Mathematics. os-3 (1): 133–141. doi:10.1093/qmath/os-3.1.133. ISSN 0033-5606.
Phillips, Eric (1933). "The zeta-function of Riemann: further developments of van der Corput's method". The Quarterly Journal of Mathematics. os-4 (1): 209–225. doi:10.1093/qmath/os-4.1.209. ISSN 0033-5606.
Rankin, R. A. (1955). "Van der Corput's method and the theory of exponent pairs". The Quarterly Journal of Mathematics. 6 (1): 147–153. doi:10.1093/qmath/6.1.147. ISSN 0033-5606.
Titchmarsh, E. C. (1942). "On the order of ζ(½+ it )". The Quarterly Journal of Mathematics. os-13 (1): 11–17. doi:10.1093/qmath/os-13.1.11. ISSN 0033-5606.
Min, Szu-Hoa (1949). "On the order of 𝜁(1/2+𝑖𝑡)". Transactions of the American Mathematical Society. 65 (3): 448–472. doi:10.1090/S0002-9947-1949-0030996-6. ISSN 0002-9947.
Haneke, W. (1963). "Verschärfung der Abschätzung von ξ(½+it)". Acta Arithmetica (in German). 8 (4): 357–430. doi:10.4064/aa-8-4-357-430. ISSN 0065-1036.
Kolesnik, Grigori (1982-01-01). "On the order of ζ (1/2+ it ) and Δ( R )". Pacific Journal of Mathematics. 98 (1): 107–122. doi:10.2140/pjm.1982.98.107. ISSN 0030-8730.
Kolesnik, G. (1985). "On the method of exponent pairs". Acta Arithmetica. 45 (2): 115–143. doi:10.4064/aa-45-2-115-143.
Huxley (2002), Huxley (2005) Huxley, M. N. (2002), "Integer points, exponential sums and the Riemann zeta function", Number theory for the millennium, II (Urbana, IL, 2000), A K Peters, pp. 275–290, MR 1956254 Huxley, M. N. (2005), "Exponential sums and the Riemann zeta function. V", Proceedings of the London Mathematical Society, Third Series, 90 (1): 1–41, doi:10.1112/S0024611504014959, ISSN 0024-6115, MR 2107036
Bourgain (2017) Bourgain, Jean (2017), "Decoupling, exponential sums and the Riemann zeta function", Journal of the American Mathematical Society, 30 (1): 205–224, arXiv:1408.5794, doi:10.1090/jams/860, MR 3556291, S2CID 118064221
Bourgain (2017) Bourgain, Jean (2017), "Decoupling, exponential sums and the Riemann zeta function", Journal of the American Mathematical Society, 30 (1): 205–224, arXiv:1408.5794, doi:10.1090/jams/860, MR 3556291, S2CID 118064221
Heath-Brown (1979) Heath-Brown, D. R. (1979), "The fourth power moment of the Riemann zeta function", Proceedings of the London Mathematical Society, Third Series, 38 (3): 385–422, doi:10.1112/plms/s3-38.3.385, ISSN 0024-6115, MR 0532980
Ingham (1928) Ingham, A. E. (1928), "Mean-Value Theorems in the Theory of the Riemann Zeta-Function", Proc. London Math. Soc., s2-27 (1): 273–300, doi:10.1112/plms/s2-27.1.273
Conrey & Ghosh (1998) Conrey, J. B.; Ghosh, A. (1998), "A conjecture for the sixth power moment of the Riemann zeta-function", International Mathematics Research Notices, 1998 (15): 775–780, arXiv:math/9807187, Bibcode:1998math......7187C, doi:10.1155/S1073792898000476, ISSN 1073-7928, MR 1639551
Keating & Snaith (2000) Keating, Jonathan P.; Snaith, N. C. (2000), "Random matrix theory and ζ(1/2+it)", Communications in Mathematical Physics, 214 (1): 57–89, Bibcode:2000CMaPh.214...57K, CiteSeerX 10.1.1.15.8362, doi:10.1007/s002200000261, ISSN 0010-3616, MR 1794265, S2CID 11095649
Cramér, Harald (1936). "On the order of magnitude of the difference between consecutive prime numbers". Acta Arithmetica. 2 (1): 23–46. doi:10.4064/aa-2-1-23-46. ISSN 0065-1036.
Banks, William; Ford, Kevin; Tao, Terence (2023). "Large prime gaps and probabilistic models". Inventiones Mathematicae. 233 (3): 1471–1518. arXiv:1908.08613. doi:10.1007/s00222-023-01199-0. ISSN 0020-9910.
Ingham, A. E. (1940). "ON THE ESTIMATION OF N (σ, T )". The Quarterly Journal of Mathematics. os-11 (1): 201–202. doi:10.1093/qmath/os-11.1.201. ISSN 0033-5606.
Huxley, M. N. (1971). "On the Difference between Consecutive Primes". Inventiones Mathematicae. 15 (2): 164–170. doi:10.1007/BF01418933. ISSN 0020-9910.
Bernstein, Joseph; Reznikov, Andre (2010-10-05). "Subconvexity bounds for triple L -functions and representation theory". Annals of Mathematics. 172 (3): 1679–1718. arXiv:math/0608555. doi:10.4007/annals.2010.172.1679. ISSN 0003-486X. S2CID 14745024.
Michel, Philippe; Venkatesh, Akshay (2010). "The subconvexity problem for GL₂". Publications Mathématiques de l'IHÉS. 111 (1): 171–271. arXiv:0903.3591. CiteSeerX 10.1.1.750.8950. doi:10.1007/s10240-010-0025-8. S2CID 14155294.

encyclopediaofmath.org

"Density hypothesis - Encyclopedia of Mathematics". encyclopediaofmath.org. Retrieved 2024-07-16.

eudml.org

Kolesnik, G. A. (1973). "On the estimation of some trigonometric sums". Acta Arithmetica (in Russian). 25 (1): 7–30. ISSN 0065-1036. Retrieved 2024-02-05.
Huxley, M. N. (1971). "On the Difference between Consecutive Primes". Inventiones Mathematicae. 15 (2): 164–170. doi:10.1007/BF01418933. ISSN 0020-9910.

harvard.edu

ui.adsabs.harvard.edu

Conrey & Ghosh (1998) Conrey, J. B.; Ghosh, A. (1998), "A conjecture for the sixth power moment of the Riemann zeta-function", International Mathematics Research Notices, 1998 (15): 775–780, arXiv:math/9807187, Bibcode:1998math......7187C, doi:10.1155/S1073792898000476, ISSN 1073-7928, MR 1639551
Keating & Snaith (2000) Keating, Jonathan P.; Snaith, N. C. (2000), "Random matrix theory and ζ(1/2+it)", Communications in Mathematical Physics, 214 (1): 57–89, Bibcode:2000CMaPh.214...57K, CiteSeerX 10.1.1.15.8362, doi:10.1007/s002200000261, ISSN 0010-3616, MR 1794265, S2CID 11095649

hathitrust.org

babel.hathitrust.org

see Lindelöf (1908) Lindelöf, Ernst (1908), "Quelques remarques sur la croissance de la fonction ζ(s)", Bull. Sci. Math., 32: 341–356
Lindelöf (1908) Lindelöf, Ernst (1908), "Quelques remarques sur la croissance de la fonction ζ(s)", Bull. Sci. Math., 32: 341–356

ias.edu

"New Bounds for Large Values of Dirichlet Polynomials, Part 1 - Videos | Institute for Advanced Study". www.ias.edu. 2024-06-04. Retrieved 2024-07-16.
"New Bounds for Large Values of Dirichlet Polynomials, Part 2 - Videos | Institute for Advanced Study". www.ias.edu. 2024-06-04. Retrieved 2024-07-16.

oup.com

academic.oup.com

Ingham, A. E. (1940). "ON THE ESTIMATION OF N (σ, T )". The Quarterly Journal of Mathematics. os-11 (1): 201–202. doi:10.1093/qmath/os-11.1.201. ISSN 0033-5606.

princeton.edu

annals.math.princeton.edu

Bernstein, Joseph; Reznikov, Andre (2010-10-05). "Subconvexity bounds for triple L -functions and representation theory". Annals of Mathematics. 172 (3): 1679–1718. arXiv:math/0608555. doi:10.4007/annals.2010.172.1679. ISSN 0003-486X. S2CID 14745024.

psu.edu

citeseerx.ist.psu.edu

Keating & Snaith (2000) Keating, Jonathan P.; Snaith, N. C. (2000), "Random matrix theory and ζ(1/2+it)", Communications in Mathematical Physics, 214 (1): 57–89, Bibcode:2000CMaPh.214...57K, CiteSeerX 10.1.1.15.8362, doi:10.1007/s002200000261, ISSN 0010-3616, MR 1794265, S2CID 11095649
Michel, Philippe; Venkatesh, Akshay (2010). "The subconvexity problem for GL₂". Publications Mathématiques de l'IHÉS. 111 (1): 171–271. arXiv:0903.3591. CiteSeerX 10.1.1.750.8950. doi:10.1007/s10240-010-0025-8. S2CID 14155294.

quantamagazine.org

Cepelewicz, Jordana (2024-07-15). "'Sensational' Proof Delivers New Insights Into Prime Numbers". Quanta Magazine. Retrieved 2024-07-16.
Hartnett, Kevin (2022-01-13). "Mathematicians Clear Hurdle in Quest to Decode Primes". Quanta Magazine. Retrieved 2022-02-17.

scientificamerican.com

Bischoff, Manon. "The Biggest Problem in Mathematics Is Finally a Step Closer to Being Solved". Scientific American. Retrieved 2024-07-16.

semanticscholar.org

api.semanticscholar.org

Bourgain (2017) Bourgain, Jean (2017), "Decoupling, exponential sums and the Riemann zeta function", Journal of the American Mathematical Society, 30 (1): 205–224, arXiv:1408.5794, doi:10.1090/jams/860, MR 3556291, S2CID 118064221
Bourgain (2017) Bourgain, Jean (2017), "Decoupling, exponential sums and the Riemann zeta function", Journal of the American Mathematical Society, 30 (1): 205–224, arXiv:1408.5794, doi:10.1090/jams/860, MR 3556291, S2CID 118064221
Keating & Snaith (2000) Keating, Jonathan P.; Snaith, N. C. (2000), "Random matrix theory and ζ(1/2+it)", Communications in Mathematical Physics, 214 (1): 57–89, Bibcode:2000CMaPh.214...57K, CiteSeerX 10.1.1.15.8362, doi:10.1007/s002200000261, ISSN 0010-3616, MR 1794265, S2CID 11095649
Bernstein, Joseph; Reznikov, Andre (2010-10-05). "Subconvexity bounds for triple L -functions and representation theory". Annals of Mathematics. 172 (3): 1679–1718. arXiv:math/0608555. doi:10.4007/annals.2010.172.1679. ISSN 0003-486X. S2CID 14745024.
Michel, Philippe; Venkatesh, Akshay (2010). "The subconvexity problem for GL₂". Publications Mathématiques de l'IHÉS. 111 (1): 171–271. arXiv:0903.3591. CiteSeerX 10.1.1.750.8950. doi:10.1007/s10240-010-0025-8. S2CID 14155294.

worldcat.org

search.worldcat.org

Hardy, G. H.; Littlewood, J. E. (1916). "Contributions to the theory of the riemann zeta-function and the theory of the distribution of primes". Acta Mathematica. 41: 119–196. doi:10.1007/BF02422942. ISSN 0001-5962.
Titchmarsh, E. C. (1932). "On van der Corput's method and the zeta-function of Riemann (III)". The Quarterly Journal of Mathematics. os-3 (1): 133–141. doi:10.1093/qmath/os-3.1.133. ISSN 0033-5606.
Phillips, Eric (1933). "The zeta-function of Riemann: further developments of van der Corput's method". The Quarterly Journal of Mathematics. os-4 (1): 209–225. doi:10.1093/qmath/os-4.1.209. ISSN 0033-5606.
Rankin, R. A. (1955). "Van der Corput's method and the theory of exponent pairs". The Quarterly Journal of Mathematics. 6 (1): 147–153. doi:10.1093/qmath/6.1.147. ISSN 0033-5606.
Titchmarsh, E. C. (1942). "On the order of ζ(½+ it )". The Quarterly Journal of Mathematics. os-13 (1): 11–17. doi:10.1093/qmath/os-13.1.11. ISSN 0033-5606.
Min, Szu-Hoa (1949). "On the order of 𝜁(1/2+𝑖𝑡)". Transactions of the American Mathematical Society. 65 (3): 448–472. doi:10.1090/S0002-9947-1949-0030996-6. ISSN 0002-9947.
Haneke, W. (1963). "Verschärfung der Abschätzung von ξ(½+it)". Acta Arithmetica (in German). 8 (4): 357–430. doi:10.4064/aa-8-4-357-430. ISSN 0065-1036.
Kolesnik, G. A. (1973). "On the estimation of some trigonometric sums". Acta Arithmetica (in Russian). 25 (1): 7–30. ISSN 0065-1036. Retrieved 2024-02-05.
Kolesnik, Grigori (1982-01-01). "On the order of ζ (1/2+ it ) and Δ( R )". Pacific Journal of Mathematics. 98 (1): 107–122. doi:10.2140/pjm.1982.98.107. ISSN 0030-8730.
Huxley (2002), Huxley (2005) Huxley, M. N. (2002), "Integer points, exponential sums and the Riemann zeta function", Number theory for the millennium, II (Urbana, IL, 2000), A K Peters, pp. 275–290, MR 1956254 Huxley, M. N. (2005), "Exponential sums and the Riemann zeta function. V", Proceedings of the London Mathematical Society, Third Series, 90 (1): 1–41, doi:10.1112/S0024611504014959, ISSN 0024-6115, MR 2107036
Heath-Brown (1979) Heath-Brown, D. R. (1979), "The fourth power moment of the Riemann zeta function", Proceedings of the London Mathematical Society, Third Series, 38 (3): 385–422, doi:10.1112/plms/s3-38.3.385, ISSN 0024-6115, MR 0532980
Conrey & Ghosh (1998) Conrey, J. B.; Ghosh, A. (1998), "A conjecture for the sixth power moment of the Riemann zeta-function", International Mathematics Research Notices, 1998 (15): 775–780, arXiv:math/9807187, Bibcode:1998math......7187C, doi:10.1155/S1073792898000476, ISSN 1073-7928, MR 1639551
Keating & Snaith (2000) Keating, Jonathan P.; Snaith, N. C. (2000), "Random matrix theory and ζ(1/2+it)", Communications in Mathematical Physics, 214 (1): 57–89, Bibcode:2000CMaPh.214...57K, CiteSeerX 10.1.1.15.8362, doi:10.1007/s002200000261, ISSN 0010-3616, MR 1794265, S2CID 11095649
Cramér, Harald (1936). "On the order of magnitude of the difference between consecutive prime numbers". Acta Arithmetica. 2 (1): 23–46. doi:10.4064/aa-2-1-23-46. ISSN 0065-1036.
Banks, William; Ford, Kevin; Tao, Terence (2023). "Large prime gaps and probabilistic models". Inventiones Mathematicae. 233 (3): 1471–1518. arXiv:1908.08613. doi:10.1007/s00222-023-01199-0. ISSN 0020-9910.
Ingham, A. E. (1940). "ON THE ESTIMATION OF N (σ, T )". The Quarterly Journal of Mathematics. os-11 (1): 201–202. doi:10.1093/qmath/os-11.1.201. ISSN 0033-5606.
Huxley, M. N. (1971). "On the Difference between Consecutive Primes". Inventiones Mathematicae. 15 (2): 164–170. doi:10.1007/BF01418933. ISSN 0020-9910.
Bernstein, Joseph; Reznikov, Andre (2010-10-05). "Subconvexity bounds for triple L -functions and representation theory". Annals of Mathematics. 172 (3): 1679–1718. arXiv:math/0608555. doi:10.4007/annals.2010.172.1679. ISSN 0003-486X. S2CID 14745024.