Distribution of mass of holomorphic cusp forms

Valentin Blomer, Rizwanur Khan, Matthew Young

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

We prove an upper bound for the L4-norm and for the L2-norm restricted to the vertical geodesic of a holomorphic Hecke cusp form f of large weight k. The method is based on Watson's formula and estimating a mean value of certain L-functions of degree 6. Further applications to restriction problems of Siegel modular forms and subconvexity bounds of degree 8 L-functions are given.

Original languageEnglish
Pages (from-to)2609-2644
Number of pages36
JournalDuke Mathematical Journal
Volume162
Issue number14
DOIs
Publication statusPublished - 1 Nov 2013
Externally publishedYes

Fingerprint

Cusp Form
L-function
Siegel Modular Forms
Norm
Mean Value
Geodesic
Vertical
Upper bound
Restriction

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Distribution of mass of holomorphic cusp forms. / Blomer, Valentin; Khan, Rizwanur; Young, Matthew.

In: Duke Mathematical Journal, Vol. 162, No. 14, 01.11.2013, p. 2609-2644.

Research output: Contribution to journalArticle

Blomer, Valentin ; Khan, Rizwanur ; Young, Matthew. / Distribution of mass of holomorphic cusp forms. In: Duke Mathematical Journal. 2013 ; Vol. 162, No. 14. pp. 2609-2644.
@article{293236e5e5e948729d13aee71d662c53,
title = "Distribution of mass of holomorphic cusp forms",
abstract = "We prove an upper bound for the L4-norm and for the L2-norm restricted to the vertical geodesic of a holomorphic Hecke cusp form f of large weight k. The method is based on Watson's formula and estimating a mean value of certain L-functions of degree 6. Further applications to restriction problems of Siegel modular forms and subconvexity bounds of degree 8 L-functions are given.",
author = "Valentin Blomer and Rizwanur Khan and Matthew Young",
year = "2013",
month = "11",
day = "1",
doi = "10.1215/00127094-2380967",
language = "English",
volume = "162",
pages = "2609--2644",
journal = "Duke Mathematical Journal",
issn = "0012-7094",
publisher = "Duke University Press",
number = "14",

}

TY - JOUR

T1 - Distribution of mass of holomorphic cusp forms

AU - Blomer, Valentin

AU - Khan, Rizwanur

AU - Young, Matthew

PY - 2013/11/1

Y1 - 2013/11/1

N2 - We prove an upper bound for the L4-norm and for the L2-norm restricted to the vertical geodesic of a holomorphic Hecke cusp form f of large weight k. The method is based on Watson's formula and estimating a mean value of certain L-functions of degree 6. Further applications to restriction problems of Siegel modular forms and subconvexity bounds of degree 8 L-functions are given.

AB - We prove an upper bound for the L4-norm and for the L2-norm restricted to the vertical geodesic of a holomorphic Hecke cusp form f of large weight k. The method is based on Watson's formula and estimating a mean value of certain L-functions of degree 6. Further applications to restriction problems of Siegel modular forms and subconvexity bounds of degree 8 L-functions are given.

UR - http://www.scopus.com/inward/record.url?scp=84888071866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888071866&partnerID=8YFLogxK

U2 - 10.1215/00127094-2380967

DO - 10.1215/00127094-2380967

M3 - Article

AN - SCOPUS:84888071866

VL - 162

SP - 2609

EP - 2644

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

SN - 0012-7094

IS - 14

ER -