Low-lying zeros of number field \(L\)-functions

DOI10.1016/j.jnt.2012.05.034zbMath1368.11116arXiv1003.5336OpenAlexW2004961068MaRDI QIDQ455799

Steven J. Miller, Ryan Peckner

Publication date: 22 October 2012

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.5336

zbMATH Keywords

symmetryclass numberHecke characterslower order terms1-level densityCM-fieldslow-lying zeros

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Zeta functions and (L)-functions of number fields (11R42) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Relations with random matrices (11M50)

Related Items

LOWER-ORDER TERMS OF THE ONE-LEVEL DENSITY OF A FAMILY OF QUADRATIC HECKE -FUNCTIONS, Some Results in the Theory of Low-Lying Zeros of Families of L-Functions, Determining optimal test functions for 2-level densities, Orthogonal and symplectic 𝑛-level densities, One-level density for holomorphic cusp forms of arbitrary level, An elliptic curve test of the \(L\)-functions ratios conjecture, A unitary test of the Ratios Conjecture, Maass Waveforms and Low-Lying Zeros, From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond, Hilbert spaces and low-lying zeros of \(L\)-functions

Cites Work

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• Low-lying zeros of \(L\)-functions with orthogonal symmetry
• Lower order terms for the one-level density of elliptic curve \(L\)-functions
• A bound for the least prime ideal in the Chebotarev density theorem
• Low-lying zeros of \(L\)-functions and random matrix theory
• Low-lying zeros of dihedral \(L\)-functions
• Counting integral ideals in a number field
• Petits zéros de fonctions L de formes modulaires
• Maass Waveforms and Low-Lying Zeros
• An orthogonal test of the L-functions Ratios Conjecture, II
• Statistics for low-lying zeros of symmetric power L-functions in the level aspect
• An orthogonal test of the L -functions Ratios conjecture
• The low lying zeros of a GL(4) and a GL(6) family of $L$-functions
• A Symplectic Test of the L-Functions Ratios Conjecture
• Lower order terms in the 1-level density for families of holomorphic cuspidal newforms
• The effect of convolving families of L -functions on the underlying group symmetries
• Zeroes of zeta functions and symmetry
• On CM-fields with the same maximal real subfield
• Inclusion of CM-fields and divisibility ofrelative class numbers
• On the Distribution of Spacings Between Zeros of the Zeta Function
• Linear Statistics of Low-Lying Zeros of L-Functions
• One- and two-level densities for rational families of elliptic curves: evidence for the underlying group symmetries
• Small zeros of quadratic L-functions
• Small generators of the ideal class group
• Low-lying zeros of families of elliptic curves
• Low lying zeros of families of \(L\)-functions