POINTWISE BOUNDS FOR EISENSTEIN SERIES ON Γ0(q)/SL2(R)

Evgeny Musicantov, Sa'ar Zehavi

Research output: Contribution to journalArticlepeer-review

Abstract

We construct pointwise bounds in the weight aspect for Eisenstein series on X0(q) = Γ0(q)\SL2(R), with squarefree level q, using a Sobolev technique. More specifically, we show that for an Eisenstein series E on X0(q) of weight parameter n and type t, one has for all x ∈ X0(q): |E(x,1/2 + it)| ≪ϵ qϵ(1 + |n|1/2+ϵ + |t|1/2+ϵ)√y(x) + y(x)−1, where y(x) is the Iwasawa y-coordinate of the point x.

Original languageEnglish
Pages (from-to)529-591
Number of pages63
JournalQuarterly Journal of Mathematics
Volume74
Issue number2
DOIs
StatePublished - 1 Jun 2023
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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