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Your search keyword '"Cusp form"' showing total 2 results
Start Over Descriptor "Cusp form" Topic automorphic l-function Publication Year Range Last 50 years Journal frontiers of mathematics in china
2 results on '"Cusp form"'

1. Mean-square estimate of automorphic L-functions.

Author

Yao, Weili

Subjects
*L-functions, *MODULAR groups, *ESTIMATES
Abstract

Let f be a holomorphic Hecke cusp form with even integral weight k ⩾ 2 for the full modular group, and let χ be a primitive Dirichlet character modulo q. Let Lf (s, χ) be the automorphic L-function attached to f and χ. We study the mean-square estimate of Lf (s, χ) and establish an asymptotic formula. [ABSTRACT FROM AUTHOR]

Published
2020
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2. Zero density of L-functions related to Maass forms

Author

Hengcai Tang

Subjects
Combinatorics, Mathematics (miscellaneous), Automorphic L-function, Mathematical analysis, Multiplicity (mathematics), SL2(R), Cusp form, Mathematics
Abstract

Let f(z) be a Hecke-Maass cusp form for SL2(ℤ), and let L(s, f) be the corresponding automorphic L-function associated to f. For sufficiently large T, let N(σ, T) be the number of zeros ρ = β +iγ of L(s, f) with |γ| ⩽ T, β ⩾ σ, the zeros being counted according to multiplicity. In this paper, we get that for 3/4 ⩽ σ ⩽ 1 − ɛ, there exists a constant C = C(ɛ) such that N(σ,T) ≪ T2(1−σ)/σ(logT)C, which improves the previous results.

Published
2013

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