Tetra and Didi, the cosmic spectral twins.
The binary additive divisor problem
The distribution of the eigenvalues of Hecke operators
The Fourier transforms of weighted orbital integrals on simisimple groups of real rank one.
The fundamental lemma of a relative trace formula for
The Laplace operator on hyperbolic three manifolds with cusps of non-maximal rank.
The Lax-Phillips infinitesimal generator and the scattering matrix for automorphic functions
We study the infinitesimal generator of the Lax-Phillips semigroup of the automorphic scattering system defined on the Poincaré upper half-plane for SL₂(ℤ). We show that its spectrum consists only of the poles of the resolvent of the generator, and coincides with the poles of the scattering matrix, counted with multiplicities. Using this we construct an operator whose eigenvalues, counted with algebraic multiplicities (i.e. dimensions of generalized eigenspaces), are precisely the non-trivial zeros...
The non-semi-simple term in the trace formula for rank one lattices.
The Selberg zeta-function for cocompact discrete subgroups of PSL(2,C)
The spectral growth of automorphic L-functions.
The spectral mean value for linear forms in twisted coefficients of cusp forms
The Spectrum of Fermat Curves.
The Trace of Hecke Operators.
Towards a stable trace formula.
Trace formula in noncommutative Geometry and the zeros of the Riemann zeta function
Trace formulae and applications to class numbers
In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2() with being the ring of integers of an imaginary quadratic number field K of class number H K > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.
Trace formulae and imaginary quadratic fields.
Trace formulas and class number sums