Pointwise bounds for eisenstein series on Γ0(q)\SL2(ℝ)

DOI10.1093/QMATH/HAAC032zbMATH Open1517.11029arXiv2112.07291OpenAlexW4308951935MaRDI QIDQ6155911

Sa'ar Zehavi, Evgeny Musicantov

Publication date: 7 June 2023

Published in: The Quarterly Journal of Mathematics (Search for Journal in Brave)

Abstract: We construct pointwise bounds in the weight aspect for Eisenstein series on $X_0(q)=Gamm{a}_0(q)setminusS{L}_2(mathbbR)$, with squarefree level $q$, using a Sobolev technique. More specifically, we show that for an Eisenstein series $E$ on $X_0(q)$ of weight parameter $n$ and type $t$, one has for all $xin{X}_0(q)$: $|E(x,1/2+it)|l{l}_{epsilon}{q}^{epsilon}(1+|n{|}^{1/2+epsilon}+|t{|}^{1/2+epsilon})sqrty(x)+y(x{)}^{-1}$, where $y(x)$ is the Iwasawa $y$-coordinate of the point $x$.

Full work available at URL: https://arxiv.org/abs/2112.07291

zbMATH Keywords

Eisenstein seriesCasimir eigenforms

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Holomorphic modular forms of integral weight (11F11)

Related Items (1)

A separation property of the zeros of Eisenstein series for SL(2, ℤ)

This page was built for publication: Pointwise bounds for eisenstein series on Γ0(q)\SL2(ℝ)

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6155911)