On some conjectures and results for the Riemann zeta-function and Hecke series
On the ?-adic representations associated to some simple Shimura varieties.
On the Analytic Continuation of Rank One Eisenstein Series.
On the asypmtotic formula of Kuznetsov and existence of generic cusp forms.
On the cuspidal cohomology of -arithmetic subgroups of reductive groups over number fields
On the Kuznetsov-Bruggeman Formula for a Hilbert Modular Surface Having One Cusp.
On the Kuznetsov-Bruggemann formula for a Hilbert modular surface having one cusp (Addendum).
On the products of Hecke L-functions of holomorphic cusp forms
On the singular set, the resolvent and Fermi's Golden Rule for finite volume hyperbolic surfaces.
On the topography of Maass waveforms for .
On theta type functions associated with the zeros of the Selberg zeta functions.
Period functions for Maass wave forms. I.
Positivity of quadratic base change -functions
We show that certain quadratic base change -functions for are non-negative at their center of symmetry.
Prime geodesic theorem.
Prime geodesic theorem
Let denote the modular group . In this paper it is proved that . The exponent improves the exponent obtained by W. Z. Luo and P. Sarnak.
Quantitative analysis of the Satake parameters of GL₂ representations with prescribed local representations
We investigate the vertical version of the Sato-Tate conjecture for some GL₂ automorphic representations over totally real fields with specified local components at a finite set of finite places.
Quantitative spectral gap for thin groups of hyperbolic isometries
Let be a subgroup of an arithmetic lattice in . The quotient has a natural family of congruence covers corresponding to ideals in a ring of integers. We establish a super-strong approximation result for Zariski-dense with some additional regularity and thickness properties. Concretely, this asserts a quantitative spectral gap for the Laplacian operators on the congruence covers. This generalizes results of Sarnak and Xue (1991) and Gamburd (2002).
Quantum ergodicity of Eigenfunctions on
Quantum unique ergodicity for Eisenstein series on
In this paper we prove microlocal version of the equidistribution theorem for Wigner distributions associated to Eisenstein series on . This generalizes a recent result of W. Luo and P. Sarnak who proves equidistribution for . The averaged versions of these results have been proven by Zelditch for an arbitrary finite-volume surface, but our proof depends essentially on the presence of Hecke operators and works only for congruence subgroups of . In the proof the key estimates come from applying...
Quantum variance for Hecke eigenforms