On the oscillatory behavior of certain arithmetic functions associated with automorphic forms

DOI10.1016/j.jnt.2011.04.014zbMath1250.11047OpenAlexW2028804193MaRDI QIDQ640021

Wladimir de Azevedo Pribitkin

Publication date: 12 October 2011

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2011.04.014

zbMATH Keywords

\(L\)-functionsautomorphic formsDirichlet seriescusp formsHecke eigenformsRankin-Selberg convolutionsentire formsoscillatory sequencesspinor zeta-functions

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Fourier coefficients of automorphic forms (11F30) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66)

Related Items (10)

The first simultaneous sign change for Fourier coefficients of Hecke-Maass forms ⋮ General $\Omega $-theorems for coefficients of $L$-functions ⋮ A note on Fourier-Jacobi coefficients of Siegel modular forms ⋮ Simultaneous sign change of Fourier-coefficients of two cusp forms ⋮ On an Oscillatory Result for the Coefficients of General Dirichlet Series ⋮ Sign changes of coefficients and sums of coefficients of \(L\)-functions ⋮ Oscillatory behavior and equidistribution of signs of Fourier coefficients of cusp forms ⋮ A note on the extended Bruinier-Kohnen conjecture ⋮ A generalization of Knopp's observation on Ramanujan's tau-function ⋮ Sign changes of coefficients of certain Dirichlet series

Uses Software

• GL(n)pack

Cites Work

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• Some remarks on the \(q\)-exponents of generalized modular functions
• The theory of Jacobi forms
• Über Betragsmittelwerte und die Fourier-Koeffizienten der ganzen automorphen Formen
• L-series of Rankin type and their functional equations
• Real zeros of quadratic Dirichlet \(L\)-functions
• On the signs of Fourier coefficients of cusp forms
• On a convolution of L-series
• Rankin-Selberg method for Siegel cusp forms
• Sign changes of Hecke eigenvalues of Siegel cusp forms of genus two
• Axiomatic Theory of L-Functions: the Selberg Class
• On the sign changes of coefficients of general Dirichlet series
• Signs of Fourier coefficients of two cusp forms of different weights
• Real zeros of real odd Dirichlet $L$-functions
• Real zeros of Dedekind zeta functions of real quadratic fields
• UNINHIBITED POINCARÉ SERIES
• Automorphic Forms and L-Functions for the GroupGL(n, R)
• Automorphe Formen als metrische Invarianten. Teil I: Automorphe Formen, metrische Verknüpfung, Eigenfunktionen linearer Funktionale

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