The arithmetic of the coefficients of half-integral weight Eisenstein series
The Dirichlet series of Koecher and Maaß and modular forms of weight 3/2.
The distribution of Fourier coefficients of cusp forms over sparse sequences
Let be the nth normalized Fourier coefficient of a holomorphic Hecke eigenform . We establish that for j = 2,3,4, which improves the previous results. For j = 2, we even establish a better result.
The local Jacquet-Langlands correspondence via Fourier analysis
Let be a locally compact non-Archimedean field, and let be a division algebra of dimension 4. The Jacquet-Langlands correspondence provides a bijection between smooth irreducible representations of of dimension and irreducible cuspidal representations of . We present a new construction of this bijection in which the preservation of epsilon factors is automatic. This is done by constructing a family of pairs , where is an order and is a finite-dimensional representation of a certain...
The Maaß Space and Hecke Operators.
The Mean Square of Dirichlet Series Associated with Automorphic Forms.
The prime number theorem in short intervals for automorphic L-functions
The q-Mellin transform of automorphic forms and converse theorems
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 Siegel-Walfisz theorem for Rankin-Selberg L-functions associated with two cusp forms
The spectral growth of automorphic L-functions.
The Spectral Mean Square of Hecke L-functions on the Critical Line
The universality of zeta-functions attached to certain cusp forms
Theta and L-function splittings
Theta-transforms and even zeta functions of Siegel modular forms