Ramanujan duals II.
Rankin-Selberg method for real analytic cusp forms of arbitrary real weight.
Regular trace formula and base change for
The “regular”trace formula, for a test function with a local component which is Iwahori-biinvariant and sufficiently regular with respect to the other components, is developed in the context of a reductive group. It is used to give a simple proof of the theory of base-change for cuspidal automorphic representations of which have a supercuspidal component. A purely local proof is given to transfer orbital integrals of sufficiently many spherical functions, by relating them to regular Iwahori functions....
Résonances
Selberg Zeta function on an exceptional domain.
Selberg's trace formula on the -regular tree and applications.
Small eigenvalues of Laplacian for
Some applications of large sieve in Riemann surfaces
Some relations between the analytical modular forms and Maass waveforms for
Some results on unipotent orbital integrals
Spectral deformations of automorphic functions over graphs of groups.
Spectral geometry and scattering theory for certain complete surfaces of finite volume.
Spectral limits for hyperbolic surfaces, I.
Spectral limits for hyperbolic surfaces, II.
Spectral theta series of operators with periodic bicharacteristic flow
The theta series is a classical example of a modular form. In this article we argue that the trace , where is a self-adjoint elliptic pseudo-differential operator of order 1 with periodic bicharacteristic flow, may be viewed as a natural generalization. In particular, we establish approximate functional relations under the action of the modular group. This allows a detailed analysis of the asymptotics of near the real axis, and the proof of logarithm laws and limit theorems for its value...
Stabilization of periods of Eisenstein series and Bessel distributions on relative to .
Strong spectral gaps for compact quotients of products of )
The existence of a strong spectral gap for quotients of noncompact connected semisimple Lie groups is crucial in many applications. For congruence lattices there are uniform and very good bounds for the spectral gap coming from the known bounds towards the Ramanujan–Selberg conjectures. If has no compact factors then for general lattices a spectral gap can still be established, but there is no uniformity and no effective bounds are known. This note is concerned with the spectral gap for an irreducible...
Sums of coefficients of Hecke series
Sums of squares in
Sur le changement de base stable des intégrales orbitales pondérées