On asymptotic behavior of generalized Li coefficients in the Selberg class

DOI10.1016/j.jnt.2010.08.009zbMath1257.11082OpenAlexW1995846713MaRDI QIDQ626841

Almasa Odžak, Lejla Smajlovic

Publication date: 18 February 2011

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2010.08.009

zbMATH Keywords

Selberg classLi's coefficients

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Zeta functions and (L)-functions (11S40)

Related Items (16)

The Li–Sekatskii coefficients for the Selberg class ⋮ Centralized variant of the Li criterion on functions fields ⋮ Unnamed Item ⋮ On asymptotic behavior of generalized Li coefficients ⋮ On the asymptotic criterion for the zero-free regions of certain $L$-functions ⋮ On the discretized Li coefficients for a certain class of \(L\)-functions ⋮ ON INTERPOLATION FUNCTIONS FOR GENERALIZED Li COEFFICIENTS IN THE SELBERG CLASS ⋮ On relations equivalent to the generalized Riemann hypothesis for the Selberg class ⋮ Evaluation of the Li coefficients on function fields and applications ⋮ Explicit bound to distinguish two \(L\)-functions ⋮ On properties of certain special zeros of functions in the Selberg class ⋮ Variations on criteria of Pólya and Turán for the Riemann hypothesis ⋮ Explicit zero-free regions and a $\tau$-Li-type criterion ⋮ On τ-Li Coefficients for Rankin–Selberg L-Functions ⋮ On the zeros of some 𝐿 functions from the extended Selberg class ⋮ On the modified Li criterion for a certain class of \(L\)-functions

Cites Work

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• A survey of the Selberg class of \(L\)-functions. I
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• The Li criterion and the Riemann hypothesis for the Selberg class. II
• On Li's coefficients for the Rankin-Selberg \(L\)-functions
• Zeta functions over zeros of zeta functions
• Local coefficients as Artin factors for real groups
• Complements to Li's criterion for the Riemann Hypothesis
• The positivity of a sequence of numbers and the Riemann hypothesis
• On the structure of the Selberg class. I: \(0\leq d\leq 1\).
• A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
• Zeros of principal \(L\)-functions and random matrix theory
• Sharpenings of Li's criterion for the Riemann hypothesis
• Li coefficients for automorphic \(L\)-functions
• Fourier Transforms of Intertwining Operators and Plancherel Measures for GL(n)
• On A. Weil's explicit formula.
• On Certain L-Functions
• On Euler Products and the Classification of Automorphic Representations I
• On Euler Products and the Classification of Automorphic Forms II
• Boundedness of automorphic 𝐿–functions in vertical strips
• Distinct zeros of functions in the Selberg class
• Zeta Functions Over Zeros of General Zeta and L-Functions

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