A mean value of a triple product of L-functions

Jack Buttcane, Rizwanur Khan

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Luo has proven an optimal upper bound for the L4-norm of dihedral Maass forms of large eigenvalue, by bounding a mean value of triple product L-functions. Motivated by this result, we study a mean value of L-functions having similar shape, and obtain for it an asymptotic with power savings. Our work may be helpful in eventually obtaining an asymptotic for the L4-norm.

Original languageEnglish
Pages (from-to)565-591
Number of pages27
JournalMathematische Zeitschrift
Volume285
Issue number1-2
DOIs
Publication statusPublished - 1 Feb 2017

Fingerprint

Triple product
L-function
Mean Value
Norm
Power Saving
Largest Eigenvalue
Upper bound
Form

Keywords

  • Automorphic forms
  • L-Functions
  • L-Norm
  • Quantum chaos

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A mean value of a triple product of L-functions. / Buttcane, Jack; Khan, Rizwanur.

In: Mathematische Zeitschrift, Vol. 285, No. 1-2, 01.02.2017, p. 565-591.

Research output: Contribution to journalArticle

Buttcane, Jack ; Khan, Rizwanur. / A mean value of a triple product of L-functions. In: Mathematische Zeitschrift. 2017 ; Vol. 285, No. 1-2. pp. 565-591.
@article{5bece212bd83413cb062b0963104d6b8,
title = "A mean value of a triple product of L-functions",
abstract = "Luo has proven an optimal upper bound for the L4-norm of dihedral Maass forms of large eigenvalue, by bounding a mean value of triple product L-functions. Motivated by this result, we study a mean value of L-functions having similar shape, and obtain for it an asymptotic with power savings. Our work may be helpful in eventually obtaining an asymptotic for the L4-norm.",
keywords = "Automorphic forms, L-Functions, L-Norm, Quantum chaos",
author = "Jack Buttcane and Rizwanur Khan",
year = "2017",
month = "2",
day = "1",
doi = "10.1007/s00209-016-1721-y",
language = "English",
volume = "285",
pages = "565--591",
journal = "Mathematische Zeitschrift",
issn = "0025-5874",
publisher = "Springer New York",
number = "1-2",

}

TY - JOUR

T1 - A mean value of a triple product of L-functions

AU - Buttcane, Jack

AU - Khan, Rizwanur

PY - 2017/2/1

Y1 - 2017/2/1

N2 - Luo has proven an optimal upper bound for the L4-norm of dihedral Maass forms of large eigenvalue, by bounding a mean value of triple product L-functions. Motivated by this result, we study a mean value of L-functions having similar shape, and obtain for it an asymptotic with power savings. Our work may be helpful in eventually obtaining an asymptotic for the L4-norm.

AB - Luo has proven an optimal upper bound for the L4-norm of dihedral Maass forms of large eigenvalue, by bounding a mean value of triple product L-functions. Motivated by this result, we study a mean value of L-functions having similar shape, and obtain for it an asymptotic with power savings. Our work may be helpful in eventually obtaining an asymptotic for the L4-norm.

KW - Automorphic forms

KW - L-Functions

KW - L-Norm

KW - Quantum chaos

UR - http://www.scopus.com/inward/record.url?scp=84975126986&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975126986&partnerID=8YFLogxK

U2 - 10.1007/s00209-016-1721-y

DO - 10.1007/s00209-016-1721-y

M3 - Article

AN - SCOPUS:84975126986

VL - 285

SP - 565

EP - 591

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 1-2

ER -