Hostname: page-component-7c8c6479df-fqc5m Total loading time: 0 Render date: 2024-03-26T23:49:50.811Z Has data issue: false hasContentIssue false

On Riesz means of the coefficients of the Rankin–Selberg series

Published online by Cambridge University Press:  01 July 1999

ALEKSANDAR IVIĆ
Affiliation:
Katedra Matematike RGF-a, Universitet u Beogradu, Djušina 7, 11000 Beograd, Serbia (Yugoslavia) e-mail: aleks@ivic.matf.bg.ac.yu, aivic@rgf.rgf.bg.ac.yu
KOHJI MATSUMOTO
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan; e-mail: kohjimat@math.nagoya-u.ac.jp, tanigawa@math.nagoya-u.ac.jp
YOSHIO TANIGAWA
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya, 464-8602, Japan; e-mail: kohjimat@math.nagoya-u.ac.jp, tanigawa@math.nagoya-u.ac.jp

Abstract

We study Δ(x; ϕ), the error term in the asymptotic formula for [sum ]n[les ]xcn, where the cns are generated by the Rankin–Selberg series. Our main tools are Voronoï-type formulae. First we reduce the evaluation of Δ(x; ϕ) to that of Δ1(x; ϕ), the error term of the weighted sum [sum ]n[les ]x(x−n)cn. Then we prove an upper bound and a sharp mean square formula for Δ1(x; ϕ), by applying the Voronoï formula of Meurman's type. We also prove that an improvement of the error term in the mean square formula would imply an improvement of the upper bound of Δ(x; ϕ). Some other related topics are also discussed.

Type
Research Article
Copyright
The Cambridge Philosophical Society 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)