The prime number theorem in short intervals for automorphic L-functions
The q-Mellin transform of automorphic forms and converse theorems
The Rationality of Holomorphic Eisenstein Series.
The rationality of the Fourier coefficients of certain Eisenstein series on tube domains (I)
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 reciprocity theorem for Dedekind-Rademacher sums
The residual spectrum of
The restriction to of a supercuspidal representation of
The Schur Multiplicator of SL(2, Z/mZ) and the Congruence Subgroup Property.
The second moment of Dirichlet twists of Hecke L-functions
The second moment of quadratic twists of modular L-functions
We study the second moment of the central values of quadratic twists of a modular -function. Unconditionally, we obtain a lower bound which matches the conjectured asymptotic formula, while on GRH we prove the asymptotic formula itself.
The second moment of the symmetric square -functions.
The Selberg trace formula for the Picard group SL(2, Z[i])
The Selberg zeta function and a local trace formula for Kleinian groups.
The Selberg zeta-function for cocompact discrete subgroups of PSL(2,C)
The shifted fourth moment of automorphic L-functions of prime power level
We prove an asymptotic formula for the fourth moment of automorphic L-functions of level , where p is a fixed prime number and ν → ∞. This is a continuation of work by Rouymi, who computed the asymptotics of the first three moments at a prime power level, and a generalization of results obtained for a prime level by Duke, Friedlander Iwaniec and Kowalski, Michel VanderKam.
The Siegel-Walfisz theorem for Rankin-Selberg L-functions associated with two cusp forms
The singular modular forms on the 27-dimensional exceptional domain.
The space of period polynomials
The spectral growth of automorphic L-functions.