An "exact" formula for the 2n-th Bernoulli number
An explicit estimate for zeros of Dedekind zeta functions
An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial
We prove an explicit formula of Atkinson type for the error term in the asymptotic formula for the mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. To deal with the case when coefficients of the Dirichlet polynomial are complex, we apply the idea of the first author in his study on mean values of Dirichlet L-functions.
An explicit Mertens' type inequality for arithmetic progressions.
An identity for sums of polylogarithm functions.
An identity involving Dedekind sums and generalized Kloosterman sums
The various properties of classical Dedekind sums have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums . The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of...
An infinite family of graphs with the same Ihara Zeta function.
An integral involving the generalized zeta function.
An isomorphism between polynomial eigenfunctions of the transfer operator and the Eichler cohomology for modular groups.
An orthogonal test of the L-functions Ratios Conjecture, II
Analogues -adiques de certaines fonctions arithmétiques
Analyse spectrale et prolongement analytique : séries d’Eisenstein, fonctions et nombre de solutions d’équations diophantiennes
Analytic and combinatoric aspects of Hurwitz polyzêtas
In this work, a symbolic encoding of generalized Di-richlet generating series is found thanks to combinatorial techniques of noncommutative rational power series. This enables to explicit periodic generalized Dirichlet generating series – particularly the coloured polyzêtas – as linear combinations of Hurwitz polyzêtas. Moreover, the noncommutative version of the convolution theorem gives easily rise to an integral representation of Hurwitz polyzêtas. This representation enables us to build the...
Analytic continuation of multiple zeta-functions and their values at non-positive integers
Analytic continuation of representations and estimates of automorphic forms.
Analytic properties of zeta functions and subgroup growth.
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...
Anwendung einer Summationsformel auf Dirichletsche Reihen und verallgemeinerte Dedekindsche Summen
Applications of special functions for the general linear group to number theory
Approximate formulae for L(1,χ)