Weighted Distribution of Low-lying Zeros of GL(2) -functions

DOI10.4153/CJM-2018-013-8zbMath1468.11112arXiv1806.05869OpenAlexW2964088485MaRDI QIDQ4625182

Publication date: 21 February 2019

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.05869

zbMATH Keywords

$L$-function low-lying zero

Mathematics Subject Classification ID

Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Holomorphic modular forms of integral weight (11F11) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (3)

Weighted one-level density of low-lying zeros of Dirichlet $L$-functions ⋮ On the distribution of Satake parameters for Siegel modular forms ⋮ A weighted one-level density of families of $L$-functions

Cites Work

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A Sato-Tate law for $\mathrm{GL}(3)$
Weighted Sato-Tate vertical distribution of the Satake parameter of Maass forms on $\mathrm{PGL}(N)$
A family of Calabi-Yau varieties and potential automorphy. II.
One-level density for holomorphic cusp forms of arbitrary level
Averages of central $L$-values of Hilbert modular forms with an application to subconvexity
On the distribution of Satake parameters of $\text{GL}_2$ holomorphic cuspidal representations
Effective equidistribution of eigenvalues of Hecke operators
Erratum: Average values of modular $L$-series via the relative trace formula
Summation methods and distribution of eigenvalues of Hecke operators
Fourier coefficients of cusp forms
Kuznietsov trace formula and weighted distribution of Hecke eigenvalues.
On the positivity of the central critical values of automorphic $L$-functions for $GL(2)$
Sato-Tate equidistribution for families of Hecke-Maass forms on $\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)$
Asymptotic behaviors of means of central values of automorphic $L$-functions for $\mathrm{GL}(2)$
Test vectors and central $L$-values for $\mathrm{GL}(2)$
Eigenvalues of Hecke operators on Hilbert modular groups
Average values of modular $L$-series via the relative trace formula
Sato-Tate theorem for families and low-lying zeros of automorphic $L$-functions. Appendix A by Robert Kottwitz, and Appendix B by Raf Cluckers, Julia Gordon and Immanuel Halupczok.
Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms
Consequences of the Gross–Zagier formulae: Stability of average L-values, subconvexity, and non-vanishing mod p
AVERAGES OF TWISTED -FUNCTIONS
The distribution of the eigenvalues of Hecke operators
An orthogonal test of the L -functions Ratios conjecture
Distribution of Hecke eigenvalues
Weighted averages of modular 𝐿-values
Petersson's trace formula and the Hecke eigenvalues of Hilbert modular forms
Zeroes of zeta functions and symmetry
Kuznetsov’s trace formula and the Hecke eigenvalues of Maass forms
Spectral means of central values of automorphic 𝐿-functions for 𝐺𝐿(2)
Local spectral equidistribution for Siegel modular forms and applications
THE QUANTITATIVE DISTRIBUTION OF HECKE EIGENVALUES
Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝
Low lying zeros of families of $L$-functions

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