Mass distribution of holomorphic cusp forms

Details Mass distribution of holomorphic cusp forms Mass distribution of holomorphic cusp forms

2012-03-12

arxiv.org/abs/1203.2573v1

Mathematics

Number Theory

21 pages

Scientific paper

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 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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