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Displaying 1 – 19 of 19

The additive divisor problem and its analogs for Fourier coefficients of cusp forms. I.

Matti Jutila (1996)

Mathematische Zeitschrift

The covolume of quaternion groups on the four-dimensional hyperbolic space

Stefan Breulmann, Volker Helmke (1996)

Acta Arithmetica

The distribution of Fourier coefficients of cusp forms over sparse sequences

Huixue Lao, Ayyadurai Sankaranarayanan (2014)

Acta Arithmetica

Let $λ_{f} (n)$ be the nth normalized Fourier coefficient of a holomorphic Hecke eigenform $f (z) \in S_{k} (Γ)$ . We establish that $\sum_{n \leq x} λ_{f}^{2} (n^{j}) = c_{j} x + O (x^{1 - 2 / ({(j + 1)}^{2} + 1)})$ for j = 2,3,4, which improves the previous results. For j = 2, we even establish a better result.

The distribution of the eigenvalues of Hecke operators

J. B. Conrey, W. Duke, D. W. Farmer (1997)

Acta Arithmetica

The equidistribution of Fourier coefficients of half integral weight modular forms on the plane

Soufiane Mezroui (2020)

Czechoslovak Mathematical Journal

Let $f = \sum_{n = 1}^{\infty} a (n) q^{n} \in S_{k + 1 / 2} (N, χ_{0})$ be a nonzero cuspidal Hecke eigenform of weight $k + \frac{1}{2}$ and the trivial nebentypus $χ_{0}$ , where the Fourier coefficients $a (n)$ are real. Bruinier and Kohnen conjectured that the signs of $a (n)$ are equidistributed. This conjecture was proved to be true by Inam, Wiese and Arias-de-Reyna for the subfamilies ${a (t n^{2})}_{n}$ , where $t$ is a squarefree integer such that $a (t) \neq 0$ . Let $q$ and $d$ be natural numbers such that $(d, q) = 1$ . In this work, we show that ${a (t n^{2})}_{n}$ is equidistributed over any arithmetic progression $n \equiv d mod q$ .

The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, II

Wladimir de Azevedo Pribitkin (2000)

Acta Arithmetica

The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, I

Wladimir de Azevedo Pribitkin (1999)

Acta Arithmetica

The Linnik conjecture. A local approach.

Vinogradov, A.I. (2004)

Zapiski Nauchnykh Seminarov POMI

The Maaß Space and Hecke Operators.

Aloys Krieg (1990)

Mathematische Zeitschrift

The Maaß spaces on the Hermitian half-space of degree 2.

Aloys Krieg (1991)

Mathematische Annalen

The Mean Square of Dirichlet Series Associated with Automorphic Forms.

Wolfgang Müller (1992)

Monatshefte für Mathematik

The reciprocal of the beta function and $G L (n, ℝ)$ Whittaker functions

Eric Stade (1994)

Annales de l'institut Fourier

In this paper we derive, using the Gauss summation theorem for hypergeometric series, a simple integral expression for the reciprocal of Euler’s beta function. This expression is similar in form to several well-known integrals for the beta function itself.We then apply our new formula to the study of $G L (n, ℝ)$ Whittaker functions, which are special functions that arise in the Fourier theory for automorphic forms on the general linear group. Specifically, we deduce explicit integral representations of “fundamental”...

Currently displaying 1 – 19 of 19

Page 1

Displaying 1 – 19 of 19

The additive divisor problem and its analogs for Fourier coefficients of cusp forms. I.

The covolume of quaternion groups on the four-dimensional hyperbolic space

The distribution of Fourier coefficients of cusp forms over sparse sequences

The distribution of the eigenvalues of Hecke operators

The equidistribution of Fourier coefficients of half integral weight modular forms on the plane

The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, II

The Fourier coefficients of modular forms and Niebur modular integrals having small positive weight, I

The Linnik conjecture. A local approach.

The Maaß Space and Hecke Operators.

The Maaß spaces on the Hermitian half-space of degree 2.

The Mean Square of Dirichlet Series Associated with Automorphic Forms.

The reciprocal of the beta function and $G L (n, ℝ)$ Whittaker functions

The Siegel-Walfisz theorem for Rankin-Selberg L-functions associated with two cusp forms

The spectral growth of automorphic L-functions.

The spectral mean value for linear forms in twisted coefficients of cusp forms

The values of a quadratic form at square-free points

The weight of half-integral weight modular forms with few non-vanishing coefficients mod l

Theta correspondence and Hecke operators relative to a quadratic extension

Theta functions on the n-fold metaplectic cover of SL (2) - the function field case.

Currently displaying 1 – 19 of 19