Results 81 to 90 of about 112 (98)
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On Fourier Coefficients of Automorphic Forms of GL(n)
International Mathematics Research Notices, 2012It 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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Automorphic forms with degenerate Fourier coefficients
American Journal of Mathematics, 1997The main theme of this paper is that singular automorphic forms on classical groups are given by theta series liftings. We establish several inequalities relating the automorphic multiplicities of a given representation and that of its abstract theta lift.
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Fourier coefficients of cusp forms and automorphic f-functions
Journal of Mathematical Sciences, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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, 1998Let \(\mathbb{H}\) 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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Automorphic forms with integral Fourier coefficients
1970The 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, 1970Let 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, 1988Geeignet 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 twisted by Fourier coefficients of automorphic cusp forms for SL(2, ℤ)
International Journal of Number Theory, 2014Let 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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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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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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1990
The aims of this chapter are to assess known explicit formulas for the Fourier coefficients of automorphic functions playing an important role in spectral theory, and transferring certain classical estimates from the theory of analytic modular forms to non-analytic parabolic forms of weight zero.
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The aims of this chapter are to assess known explicit formulas for the Fourier coefficients of automorphic functions playing an important role in spectral theory, and transferring certain classical estimates from the theory of analytic modular forms to non-analytic parabolic forms of weight zero.
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