On the oscillatory behavior of certain arithmetic functions associated with automorphic forms
type: Item
instance of: scholarly article
title: On the oscillatory behavior of certain arithmetic functions associated with automorphic forms
zbMATH Open document ID: 1250.11047
author: Wladimir de Azevedo Pribitkin
published in: Journal of Number Theory
publication date: 2011-10-12T00:00:00Z
review text: In this work, the author derives some results related to oscillatory behavior of certain arithmetic functions associated with automorphic forms. Specifically, he examines general \(L\)-functions conjectured to satisfy the Grand Riemann Hypothesis, Dirichlet series associated with classical entire forms of real weight and multiplier system, Rankin-Selberg convolutions (both ``naive'' and ``modified''), and spinor zeta-functions of Hecke eigenforms on the Siegel modular group of genus two. For the second class he extends results obtained previously and jointly by M. Knopp, W. Kohnen, and the author, whereas for the fourth class he provides a new proof of a relatively recent result of W. Kohnen.
reviewed by: Ahmet Tekcan
Mathematics Subject Classification ID: 11F30
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F66
zbMATH DE Number: 5957005
zbMATH Keywords: oscillatory sequences
zbMATH Keywords: Dirichlet series
zbMATH Keywords: automorphic forms
zbMATH Keywords: \(L\)-functions
zbMATH Keywords: entire forms
zbMATH Keywords: cusp forms
zbMATH Keywords: Rankin-Selberg convolutions
zbMATH Keywords: Hecke eigenforms
zbMATH Keywords: spinor zeta-functions
describes a project that uses: GL(n)pack
MaRDI profile type: Publication
full work available at URL: j.jnt.2011.04.014
OpenAlex ID: W2028804193
cites work: Real zeros of Dedekind zeta functions of real quadratic fields
cites work: Real zeros of quadratic Dirichlet \(L\)-functions
cites work: The theory of Jacobi forms
cites work: Automorphic Forms and L-Functions for the GroupGL(n, R)
cites work: Q4350164
cites work: Q4830109
cites work: Axiomatic Theory of L-Functions: the Selberg Class
cites work: Q3838156
cites work: On the signs of Fourier coefficients of cusp forms
cites work: Sign changes of Hecke eigenvalues of Siegel cusp forms of genus two
cites work: Some remarks on the \(q\)-exponents of generalized modular functions
cites work: Signs of Fourier coefficients of two cusp forms of different weights
cites work: Q5568135
cites work: L-series of Rankin type and their functional equations
cites work: Q4693061
cites work: On a convolution of L-series
cites work: Automorphe Formen als metrische Invarianten. Teil I: Automorphe Formen, metrische Verknüpfung, Eigenfunktionen linearer Funktionale
cites work: Über Betragsmittelwerte und die Fourier-Koeffizienten der ganzen automorphen Formen
cites work: UNINHIBITED POINCARÉ SERIES
cites work: On the sign changes of coefficients of general Dirichlet series
cites work: Q5774823
cites work: Q4154638
cites work: Real zeros of real odd Dirichlet $L$-functions
cites work: Rankin-Selberg method for Siegel cusp forms
DOI: 10.1016/J.JNT.2011.04.014
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description: scientific article; zbMATH DE number 5957005