Surpassing the ratios conjecture in the 1-level density of Dirichlet \(L\)-functions

DOI10.2140/ant.2015.9.13zbMath1352.11079arXiv1111.3896OpenAlexW2004561412WikidataQ122915454 ScholiaQ122915454MaRDI QIDQ2018348

Steven J. Miller, Daniel Fiorilli

Publication date: 14 April 2015

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.3896

zbMATH Keywords

primes in arithmetic progressionsrandom matrix theoryDirichlet \(L\)-functionslow-lying zerosratios conjecture

Mathematics Subject Classification ID

Random matrices (algebraic aspects) (15B52) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Primes in congruence classes (11N13) Rate of growth of arithmetic functions (11N56) Relations with random matrices (11M50)

Related Items (17)

Omega results for cubic field counts via lower-order terms in the one-level density ⋮ Low-lying zeros of cubic Dirichlet \(L\)-functions and the ratios conjecture ⋮ Optimal test functions for detecting central point vanishing over families of \(L\)-functions ⋮ Small zeros of Dirichlet \(L\)-functions of quadratic characters of prime modulus ⋮ \(n\)-level density of the low-lying zeros of primitive Dirichlet \(L\)-functions ⋮ Zeros of quadratic Dirichlet $L$-functions in the hyperelliptic ensemble ⋮ One-level density estimates for Dirichlet \(L\)-functions with extended support ⋮ Some Results in the Theory of Low-Lying Zeros of Families of L-Functions ⋮ Determining optimal test functions for 2-level densities ⋮ Low-lying zeros of elliptic curve L-functions: Beyond the Ratios Conjecture ⋮ Explicit formulas for the spectral side of the trace formula of ${\rm SL(2)}$ ⋮ Orthogonal and symplectic 𝑛-level densities ⋮ One-level density of families of elliptic curves and the Ratios Conjecture ⋮ One-level density for holomorphic cusp forms of arbitrary level ⋮ Maass Waveforms and Low-Lying Zeros ⋮ Dirichlet characters and low-lying zeros of \(L\)-functions ⋮ Low-lying zeros of quadratic Dirichlet -functions: lower order terms for extended support

This page was built for publication: Surpassing the ratios conjecture in the 1-level density of Dirichlet \(L\)-functions