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

Research output: Contribution to journal › Article (Academic Journal) › peer-review

8 Citations (Scopus)

226 Downloads (Pure)

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

Access to Document

10.1515/forum-2018-0014

Full-text PDF (final published version)
This is the final published version of the article (version of record). It first appeared online via De Gruyter at https://doi.org/10.1515/forum-2018-0014 . Please refer to any applicable terms of use of the publisher.
Final published version, 1.04 MBLicence: Other

Handle.net

Persistent link

Cite this

@article{27c45879d1c84d5f822297a874db3b34,

title = "On sup-norm bounds part II: GL(2) Eisenstein series",

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

keywords = "amplification, Eisenstein series, number fields, Sup-norm",

author = "Edgar Assing",

year = "2019",

month = jul,

day = "1",

doi = "10.1515/forum-2018-0014",

language = "English",

volume = "31",

pages = "971–1006",

journal = "Forum Mathematicum",

issn = "0933-7741",

publisher = "Walter de Gruyter GmbH",

number = "4",

}

TY - JOUR

T1 - On sup-norm bounds part II

T2 - GL(2) Eisenstein series

AU - Assing, Edgar

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

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.

KW - amplification

KW - Eisenstein series

KW - number fields

KW - Sup-norm

UR - https://www.scopus.com/pages/publications/85065727228

U2 - 10.1515/forum-2018-0014

DO - 10.1515/forum-2018-0014

M3 - Article (Academic Journal)

AN - SCOPUS:85065727228

SN - 0933-7741

VL - 31

SP - 971

EP - 1006

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 4

ER -

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

Abstract

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

Cite this