Zero density estimates for automorphic \(L\)-functions of \(\mathrm{GL}_m\)

DOI10.1007/s10474-015-0548-zzbMath1363.11068OpenAlexW2141084993MaRDI QIDQ343301

Huafeng Liu, L. L. Dong, Deyu Zhang

Publication date: 25 November 2016

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-015-0548-z

zbMATH Keywords

Riemann zeta functioncusp formMaass formautomorphic \(L\)-function\(SL_2(Z)\), \(SL_3(Z)\)zero density

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items

\(\Omega\)-result for the index of composition of an integral ideal ⋮ Some density results on sets of primes for Hecke eigenvalues ⋮ Power moments of automorphic \(L\)-functions related to Maass forms for \(\mathrm{SL}_3 (\mathbb{Z})\) ⋮ On the distribution of Hecke eigenvalues over Piatetski-Shapiro prime twins ⋮ Divisor problems related to Hecke eigenvalues in three dimensions

Uses Software

• GL(n)pack

Cites Work

• Bounds for \(\mathrm{GL}(3) \times \mathrm{GL}(2)\) \(L\)-functions and \(\mathrm{GL}(3)\) \(L\)-functions
• Zero density for automorphic \(L\)-functions
• Zeros of principal \(L\)-functions and random matrix theory
• Topics in multiplicative number theory
• Zeta functions of simple algebras
• The fourth power moment of automorphic $L$-functions for $GL(2)$ over a short interval
• A new bound K2/3+  for Rankin-Selberg L-functions for Hecke congruence subgroups
• The square mean of Dirichlet series associated with cusp forms
• Zero-density estimates for L-functions
• The Fourth Power Moment of the Riemann Zeta Function
• Automorphic Forms and L-Functions for the GroupGL(n, R)
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