Results 121 to 130 of about 260 (137)

Fourier Coefficients of Automorphic Forms

Lecture Notes in Mathematics, 1981
exaly   +3 more sources

On Fourier Coefficients of Automorphic Forms of GL(n)

International Mathematics Research Notices, 2012
It is a well-known theorem, due to J. Shalika and I. Piatetski-Shapiro, independently, that any non-zero cuspidal automorphic form on GLn(A) is generic, i.e. has a non-zero WhittakerFourier coefficient. Its proof follows from the Fourier expansion of the cuspidal automorphic form in terms of its Whittaker-Fourier coefficients.
Dihua Jiang, Baiying Liu
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Fourier coefficients of cusp forms and automorphic f-functions

Journal of Mathematical Sciences, 1999
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Exponential sums with Fourier coefficients of automorphic forms

Mathematische Zeitschrift, 2017
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Averages Involving Fourier Coefficients of Non-Analytic Automorphic Forms

Canadian Mathematical Bulletin, 1970
Let f(τ) be a complex valued function, defined and analytic in the upper half of the complex τ plane (τ=x+iy, y > 0), such that f(τ+λ) = f(τ) where λ is real and f(-1/τ) = γ(-iτ)k f(τ), k being a complex number.
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Automorphic forms with integral Fourier coefficients

1970
The purpose of this note is to prove that under certain hypotheses, the graded ring of integral automorphic forms, with respect to an arithmetic group operating On a tube domain, is generated as a graded algebra over the complex numbers by a finite number of automorphic forms having rational integral Fourier coefficients.
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Exponential sums formed with the von Mangoldt function and Fourier coefficients of $${ GL}(m)$$ G L ( m ) automorphic forms

Monatshefte für Mathematik, 2017
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Yujiao Jiang, Guangshi Lü
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Exponential sums twisted by Fourier coefficients of automorphic cusp forms for SL(2, ℤ)

International Journal of Number Theory, 2014
Let f be a holomorphic cusp form of weight k for SL(2, ℤ) with Fourier coefficients λf(n). We study the sum ∑n>0λf(n)ϕ(n/X)e(αn), where [Formula: see text]. It is proved that the sum is rapidly decaying for α close to a rational number a/q where q2 < X1-ε.
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On Fourier coefficients associated to automorphic L-functions over a binary quadratic form and its applications

The Ramanujan Journal
Let \(f\) and \(g\) be two distinct normalized primitive Hecke cusp forms of even integral weights \(k_1\) and \(k_2\) for the full modular group \(\mathrm{SL}_2(\mathbb{Z})\). Denote by \(\lambda_{f \otimes f \otimes f \otimes g}(n)\) the \(n\)th normalized coefficient of the automorphic \(L\)-functions \(L(f \otimes f \otimes f \otimes g, s)\). Let \(
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A reduction principle for Fourier coefficients of automorphic forms

Mathematische Zeitschrift, 2021
Dmitry Gourevitch, Henrik P A Gustafsson, Axel Kleinschmidt   +2 more
exaly