Search

Your search keyword '"Cusp form"' showing total 2 results
2 results on '"Cusp form"'

1. Fourier coefficients of symmetric power L-functions.

Author

Tang, Hengcai and Wu, Jie

Subjects
*FOURIER analysis, *COEFFICIENTS (Statistics), *MATHEMATICAL symmetry, *L-functions, *INTEGRALS, *MODULAR groups
Abstract

Let f be a Hecke eigencusp form of even integral weight k or Maass cusp form for the full modular group S L 2 ( Z ) . Denote by λ sym m f ( n ) the n th normalized coefficient of the Dirichlet expansion of the m th symmetric power L -function associated to f . In this paper, we establish some bounds for ∑ n ⩽ x λ sym m f ( n ) , ∑ n ⩽ x λ f ( n m ) , which improve the corresponding results of Lau & Lü [8] . [ABSTRACT FROM AUTHOR]

Published
2016
Full Text
View/download PDF

2. Distribution of mass of holomorphic cusp forms

Author

Rizwanur Khan, Valentin Blomer, and Matthew P. Young

Subjects
Cusp (singularity), Pure mathematics, Degree (graph theory), Distribution (number theory), Mathematics - Number Theory, General Mathematics, Mathematics::Number Theory, 010102 general mathematics, Holomorphic function, 11F11, 11F66, 01 natural sciences, Upper and lower bounds, Cusp form, 11F11, 11F66, Norm (mathematics), 0103 physical sciences, FOS: Mathematics, Number Theory (math.NT), 010307 mathematical physics, 0101 mathematics, Mathematics, Siegel modular form
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 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., 23 pages

Published
2012

Catalog

Books, media, physical & digital resources
See catalog results