On sup-norm bounds part II: GL(2) Eisenstein series

Edgar Assing

doi:10.1515/forum-2018-0014

On sup-norm bounds part II: GL(2) Eisenstein series

Edgar Assing^*

^*Corresponding author for this work

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Abstract

In this paper we consider the sup-norm problem in the context of analytic Eisenstein series for GL 2 {\mathrm{GL}-{2}} over number fields. We prove a hybrid bound which is sharper than the corresponding bound for Maaß forms. Our results generalize those of Huang and Xu where the case of Eisenstein series of square-free levels over the base field {\operatorname{\mathbb{Q}}} had been considered.

Original language	English
Pages (from-to)	971–1006
Number of pages	36
Journal	Forum Mathematicum
Volume	31
Issue number	4
Early online date	7 May 2019
DOIs	https://doi.org/10.1515/forum-2018-0014
Publication status	Published - 1 Jul 2019

Keywords

amplification
Eisenstein series
number fields
Sup-norm

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AB - In this paper we consider the sup-norm problem in the context of analytic Eisenstein series for GL 2 {\mathrm{GL}-{2}} over number fields. We prove a hybrid bound which is sharper than the corresponding bound for Maaß forms. Our results generalize those of Huang and Xu where the case of Eisenstein series of square-free levels over the base field {\operatorname{\mathbb{Q}}} had been considered.

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KW - Eisenstein series

KW - number fields

KW - Sup-norm

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On sup-norm bounds part II: GL(2) Eisenstein series

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