Results 111 to 120 of about 167,541,873 (127)

Fourier coefficients of cusp forms and automorphic f-functions

Journal of Mathematical Sciences, 1999
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Sobolev norms of automorphic functionals and Fourier coefficients of cusp forms

Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1998
Let \(\mathbb{H}\) be the upper half-plane, and fix a discrete subgroup \(\Gamma\) of \(G= PSL(2,\mathbb{R})\) such that \(Y:= \Gamma\setminus\mathbb{H}\) is a compact Riemann surface. (The authors point out that the results of the paper under review also hold for cofinite groups \(\Gamma\).) Any eigenfunction \(\phi\) of the Laplacian on \(Y\) defines
Bernstein, Joseph, Reznikov, André
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Exponential sums with Fourier coefficients of automorphic forms

Mathematische Zeitschrift, 2017
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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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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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On the Fourier coefficients of automorphic forms of triangle groups

Kobe Journal of Mathematics, 1988
Geeignet normierte automorphe Funktionen lassen sich in elliptischen und parabolischen Fixpunkten von Dreiecksgruppen in der Form \(\sum_{n\gg - \infty}a_ nr^ nq^ n\) nach der zugehörigen Ortsuniformisierenden q entwickeln, wobei die \(a_ n\) rational gewählt werden können und r nur von der Gruppe und dem gewählten Fixpunkt abhängt.
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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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Sums of Fourier coefficients of automorphic cusp forms

2022
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