Subconvexity for Rankin-Selberg \(L\)-functions of Maass forms.
type: Item
instance of: scholarly article
title: Subconvexity for Rankin-Selberg \(L\)-functions of Maass forms.
zbMATH Open document ID: 1066.11020
author: Yangbo Ye
author: Jianya Liu
published in: Geometric and Functional Analysis. GAFA
publication date: 2003-10-14T00:00:00Z
review text: The purpose of this paper is to give a subconvexity bound for Rankin-Selberg \(L\)-functions \(L(s,f\otimes g)\), where \(g\) is a fixed cusp form (holomorphic or real analytic) and \(f\) is a variable Maass cusp form with the spectral parameter tending to infinity. The forms are modular either for the full modular group or more generally for a congruence subgroup. An analogous subconvexity estimate was obtained by \textit{P. Sarnak} [J. Funct. Anal. 184 No. 2, 419--453 (2001; Zbl 1006.11022)] in the weight aspect if \(f\) is holomorphic. However, it was pointed out in the preprint ``Improvement to subconvexity bounds for Rankin-Selberg \(L\)-functions of cusp forms'' by \textit{Yuk-Kam Lau}, \textit{Jianya Liu} and \textit{Yangbo Ye} that there is a gap in the present paper so that the argument yields only a weaker estimate; nevertheless, it is stronger than the convexity bound. A better estimate is obtained in the above mentioned preprint.
reviewed by: Matti Jutila
Mathematics Subject Classification ID: 11F66
zbMATH DE Number: 1925570
zbMATH Keywords: Rankin-Selberg \(L\)-function
zbMATH Keywords: subconvexity
zbMATH Keywords: Maass form
MaRDI profile type: Publication
full work available at URL: s00039-002-1296-0
OpenAlex ID: W2130267689
DOI: 10.1007/S00039-002-1296-0
Recommended article: Subconvexity bounds for Rankin-Selberg \(L\)-functions for congruence subgroups
Recommended article: The subconvexity problem for Rankin-Selberg \(L\)-functions and equidistribution of Heegner points
Recommended article: Level Aspect Subconvexity For Rankin-Selberg $L$-functions
Recommended article: The subconvexity problem for Rankin-Selberg \(L\)-functions and equidistribution of Heegner points. II
Recommended article: A Relation Involving Rankin–Selberg L-Functions of Cusp Forms and Maass Forms
Recommended article: Subconvexity for modular form \(L\)-functions in the \(t\) aspect
Recommended article: RANKIN–SELBERG CONVOLUTIONS OF NONCUSPIDAL HALF-INTEGRAL WEIGHT MAASS FORMS IN THE PLUS SPACE
Recommended article: Double square moments and subconvexity bounds for Rankin-Selberg \(L\)-functions of holomorphic cusp forms
Recommended article: Q4409704
Recommended article: On the nonvanishing of Rankin-Selberg \(L\)-functions
description: scientific article; zbMATH DE number 1925570