TY - JOUR
T1 - POINTWISE BOUNDS FOR EISENSTEIN SERIES ON Γ0(q)/SL2(R)
AU - Musicantov, Evgeny
AU - Zehavi, Sa'ar
N1 - Publisher Copyright:
© The Author(s) 2022. Published by Oxford University Press. All rights reserved.
PY - 2023/6/1
Y1 - 2023/6/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85162078201&partnerID=8YFLogxK
U2 - 10.1093/qmath/haac032
DO - 10.1093/qmath/haac032
M3 - Article
AN - SCOPUS:85162078201
SN - 0033-5606
VL - 74
SP - 529
EP - 591
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
IS - 2
ER -