Distribution of mass of holomorphic cusp forms

2012/03/31 by Valentin Blomer, Rizwanur Khan, Matthew Young · 1 citation
Mathematics · #math.NT #msc:11F11 #msc:11F66

paper · pdf · doi:10.1215/00127094-2380967

published as Duke Math. J. 162, no. 14 (2013), 2609-2644 · 23 pages

arxiv created 2013/02/22 · arxiv updated 2019/12/19

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 of large weight. 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.

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• On the L² restriction norm of large level