Distribution of mass of holomorphic cusp forms

Valentin Blomer, Rizwanur Khan, Matthew Young

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35 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

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ASJC Scopus subject areas

  • Mathematics(all)

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