Duke Mathematical Journal· 2013Q1
Distribution of mass of holomorphic cusp forms
- 145citations
- Q1SCImago
- 2013year
Short summary
A new upper bound is established for the L4-norm and the L2-norm on the vertical geodesic of holomorphic Hecke cusp forms with large weight k.
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Key points
- Establishes an upper bound for the L4-norm of holomorphic Hecke cusp forms.
- Establishes an upper bound for the L2-norm on the vertical geodesic of holomorphic Hecke cusp forms.
- The method uses Watson's formula and estimates mean values of degree 6 L-functions.
- Applications include restriction problems for Siegel modular forms and subconvexity bounds for degree 8 L-functions.
AI-generated from the title and abstract; the full text is not read.
Abstract
We prove an upper bound for the L 4 -norm and for the L 2 -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.
The authors' abstract, as published at the source. Duke Mathematical Journal, 2013 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics