A note on the Rankin-Selberg method for Siegel cusp forms of genus 2
type: Item
instance of: scholarly article
title: A note on the Rankin-Selberg method for Siegel cusp forms of genus 2
zbMATH Open document ID: 0942.11028
author: Taro Horie
published in: Proceedings of the Japan Academy. Series A
publication date: 1999-06-29T00:00:00Z
review text: \textit{W. Kohnen} and \textit{N.-P. Skoruppa} [Invent. Math. 95, 541-558 (1989; Zbl 0665.10019)] introduced a Dirichlet series \(D_{F,G}(s)\) associated with a pair of Siegel cusp forms \((F,G)\) of genus 2 and weight \(k\). It is defined by the Petersson scalar products of the Fourier-Jacobi coefficients of \(F\) and \(G\). If the first Fourier-Jacobi coefficient of \(F\) is not zero, then \(G\) can be chosen such that \(D_{F,G}(s)\) is proportional to the spinor zeta function of \(F\). In the paper under review the author applies these methods to the case that \(F\) and \(G\) are of level \(N\geq 1\).
Mathematics Subject Classification ID: 11F46
Mathematics Subject Classification ID: 11F66
zbMATH DE Number: 1310587
zbMATH Keywords: Siegel modular form
zbMATH Keywords: Rankin-selberg method
zbMATH Keywords: Poincaré series
zbMATH Keywords: Saito-Kurokawa-Maaß lift
zbMATH Keywords: spinor zeta function
reviewed by: Aloys Krieg
MaRDI profile type: Publication
full work available at URL: pjaa.75.18
OpenAlex ID: W2077775190
cites work: Q3754056
cites work: The theory of Jacobi forms
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cites work: Heegner points and derivatives of \(L\)-series. II
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cites work: A certain Dirichlet series attached to Siegel modular forms of degree two
cites work: On the poles of Andrianov L-functions
DOI: 10.3792/PJAA.75.18
description: scientific article; zbMATH DE number 1310587