Results 81 to 90 of about 6,212 (114)

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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On Fourier coefficients of automorphic forms of symplectic groups

manuscripta mathematica, 2003
For a number of reasons it is interesting to determine Fourier coefficients of automorphic forms. The best known Fourier coefficient is the so-called Whittaker Fourier coefficient. While every cuspidal representation of \(\text{GL}_n(\mathbb A)\) has such a Fourier coefficient, for other classical groups this is not true. In the paper under the review,
Ginzburg, D., Rallis, S., Soudry, D.
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Fourier coefficients of cusp forms and automorphic f-functions

Journal of Mathematical Sciences, 1999
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Sums of k-th powers and the Whittaker–Fourier coefficients of automorphic forms

The Ramanujan Journal, 2021
The author begins this paper by briefly reviewing the literature on shifted convolution sums. Letting \(\tau_2(n) := \sum_{d_1 d_2 = n} 1\) is the number of divisors of \(n\), Luo reminds the reader that \[ \sum_{n \leq x} \tau_2(n) \tau_2(n+1) \sim \frac{6}{\pi^2} x (\log x)^2 \] as well as some generalizations and strengthenings of this result.
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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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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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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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Harmonic Analysis of Automorphic Functions. Estimates for Fourier Coefficients of Parabolic Forms of Weight Zero

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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