A generalization of Lerch’s formula
We give higher-power generalizations of the classical Lerch formula for the gamma function.
A limit theorem for the Hurwitz zeta-function with algebraic irrational parameter.
A -logarithmic analogue of Euler’s sine integral
A spectral analysis of automorphic distributions and Poisson summation formulas
Automorphic distributions are distributions on , invariant under the linear action of the group . Combs are characterized by the additional requirement of being measures supported in : their decomposition into homogeneous components involves the family , of Eisenstein distributions, and the coefficients of the decomposition are given as Dirichlet series . Functional equations of the usual (Hecke) kind relative to turn out to be equivalent to the invariance of the comb under some modification...
Absolute derivations and zeta functions.
Algebraic relations between special values of multiple sine functions
An Asymptotic Formula for a sum Involving Zeros of the Riemann Zeta-function
An isomorphism between polynomial eigenfunctions of the transfer operator and the Eichler cohomology for modular groups.
Analytic torsions on contact manifolds
We propose a definition for analytic torsion of the contact complex on contact manifolds. We show it coincides with Ray–Singer torsion on any -dimensional CR Seifert manifold equipped with a unitary representation. In this particular case we compute it and relate it to dynamical properties of the Reeb flow. In fact the whole spectral torsion function we consider may be interpreted on CR Seifert manifolds as a purely dynamical function through Selberg-like trace formulae, that hold also in variable...
Artin formalism for Selberg zeta functions of co-finite Kleinian groups
Let be a finite-volume quotient of the upper-half space, where is a discrete subgroup. To a finite dimensional unitary representation of one associates the Selberg zeta function . In this paper we prove the Artin formalism for the Selberg zeta function. Namely, if is a finite index group extension of in , and is the induced representation, then . In the second part of the paper we prove by a direct method the analogous identity for the scattering function, namely , for an appropriate...
Cramer functions and Guinand equations
Cycles on Siegel threefolds and derivatives of Eisenstein series
Dirichlet Series and Gamma Function Associated with Rational Functions
We investigate zeta regularized products of rational functions. As an application, we obtain the asymptotic expansion of the Euler Gamma function associated with a rational function.
Dynamics of the continued fraction map and the spectral theory of SL (2, Z).
Euler constants for a Fuchsian group of the first kind
Explicit estimates for the summatory function of Λ(n)/n from the one of Λ(n)
We prove that the error term differs from (ψ(x)-x)/x by a well controlled function. We deduce very precise numerical results from the formula obtained.
Fourier expansions of complex-valued Eisenstein series on finite upper half planes.
Group cohomology and the singularities of the Selberg zeta function associated to a Kleinian group.
Higher regularizations of zeros of cuspidal automorphic -functions of
We establish “higher depth” analogues of regularized determinants due to Milnor for zeros of cuspidal automorphic -functions of over a general number field. This is a generalization of the result of Deninger about the regularized determinant for zeros of the Riemann zeta function.
Hyperbolic lattice-point counting and modular symbols
For a cocompact group of we fix a real non-zero harmonic -form . We study the asymptotics of the hyperbolic lattice-counting problem for under restrictions imposed by the modular symbols . We prove that the normalized values of the modular symbols, when ordered according to this counting, have a Gaussian distribution.