The Mean Square of Dirichlet Series Associated with Automorphic Forms.
The reciprocal of the beta function and Whittaker functions
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 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”...
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.
Über das quadratische Spektralmittel von Fourierkoeffizienten reell-analytischer automorpher Formen halbzahligen Gewichts.
Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen II.
Über die Fourier-Jacobi-Entwicklung Siegelscher Eisensteinreihen.
Über die Fourrierkoeffizienten des Siegelschen Eisensteinreihen.
Über gewisse Siegelsche Modulformen zweiten Grades.
Uniform bounds for Fourier coefficients of theta-series with arithmetic applications
Uniformization of triangle modular curves.
In the present article, we determine explicit uniformizations of modular curves attached to triangle Fuchsian groups with cusps. Their Hauptmoduln are obtained by integration of non-linear differential equations of the third order. Series expansions involving integral coefficients are calculated around the cusps as well as around the elliptic points. The method is an updated form of a differential construction of the elliptic modular function j, first performed by Dedekind in 1877. Subtle differences...
Ω-results for sums of Fourier coefficients of cusp forms
Неоднородные свертки Ранкина
О связи собственных чисел операторов Гекке и коэффициентов Фурье собственных функций для зигелевых модулярных форм рода
Применения формулы Петерсона для билинейной формы от коэффициентов Фурье параболических форм