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pro vyhledávání: '"J. B. Conrey"'
Random matrix theory is an area of mathematics first developed by physicists interested in the energy levels of atomic nuclei, but it can also be used to describe some exotic phenomena in the number theory of elliptic curves. The purpose of this book
Autor:
M. A. Holmstrom, J. B. Conrey
Publikováno v:
Experimental Mathematics. 30:447-452
Let Qa(z) be the set of z-smooth numbers of the form q2+a. It is not obvious, but this is a finite set. The cardinality can be quite large; for example, |Q1(1900)|≥646890. We have a remarkably simp...
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https://explore.openaire.eu/search/publication?articleId=doi_________::2fb8348e27e66f59b72b20e738544d46
https://doi.org/10.1080/10586458.2018.1559775
https://doi.org/10.1080/10586458.2018.1559775
Autor:
J. B. Conrey, Nina C Snaith
Publikováno v:
Communications in Mathematical Physics. 330:639-653
In this paper we examine n-correlation for either the eigenvalues of a unitary group of random matrices or for the zeros of a unitary family of L-functions in the important situation when the correlations are detected via test functions whose Fourier
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https://explore.openaire.eu/search/publication?articleId=doi_________::3341cd1579638ef4fdebe60b145bd6bc
https://doi.org/10.1007/s00220-014-1969-1
https://doi.org/10.1007/s00220-014-1969-1
Publikováno v:
Experimental Mathematics. 22:195-202
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d6b0e00ee449573bf83c3040f9c40995
https://doi.org/10.1080/10586458.2013.768483
https://doi.org/10.1080/10586458.2013.768483
Autor:
Henryk Iwaniec, J. B. Conrey
Publikováno v:
Conrey, J B & Iwaniec, H 2020, ' Critical zeros of lacunary L-functions ', Acta Arithmetica, vol. 195, no. 3, pp. 217-268 . https://doi.org/10.4064/aa180813-11-11
Assuming the existence of a sequence of exceptional discriminants of quadratic fields, we show that a hundred percent of zeros of the Riemann zeta function are on the critical line in specific segments. This is a special case of a more general statem
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b8c5ee3df15ce8dd0912679a52c03693
Publikováno v:
Geometric and Functional Analysis. 22:1257-1288
We prove a formula, with power savings, for the sixth moment of Dirichlet L- functions averaged over all primitive characters χ (mod q) with q ≤ Q, and over the critical line. Our formula agrees precisely with predictions motivated by random matri
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https://doi.org/10.1007/s00039-012-0191-6
https://doi.org/10.1007/s00039-012-0191-6
Publikováno v:
International Mathematics Research Notices. 2013:4758-4771
We show that all but five of the zeros of the period polynomial associated to a Hecke cusp form are on the unit circle.
Externí odkaz:
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https://doi.org/10.1093/imrn/rns183
https://doi.org/10.1093/imrn/rns183
Publikováno v:
Acta Arithmetica. 155:353-371
We use the asymptotic large sieve, developed by the authors, to prove that if the Generalized Riemann Hypothesis is true, then there exist many Dirichlet L-functions that have a pair of consecutive zeros closer together than 0.37 times their average
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https://doi.org/10.4064/aa155-4-2
https://doi.org/10.4064/aa155-4-2
Publikováno v:
Journal of Number Theory. 128(6):1516-1554
We describe an algorithm for obtaining explicit expressions for lower terms for the conjectured full asymptotics of the moments of the Riemann zeta function, and give two distinct methods for obtaining numerical values of these coefficients. We also
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