Related papers: A proof of Hadjicostas's conjecture

New integral formulas involving the Meijer $G$-function are derived using recent results concerning distributional characterisations and distributional transformations in probability theory.

Using recent results, we prove strong multiplicity one theorems for Goss zeta functions and their Teichmuller lifts.

In this paper we present many new families of identities for multiple harmonic sums using binomial coefficients. Some of these generalize a few recent results of Hessami Pilehrood et al. As applications we prove several conjectures…

In this paper, we prove a conjecture of Andrews and Bachraoui relating a generating function arising from two-color partitions (with odd smallest part and restrictions on the even parts) to a Hecke-type double sum. Our proof is based on…

In this paper the circulant Hadamard conjecture is proved.

This note is a short survey of two topics: Archimedean zeta functions and Archimedean oscillatory integrals. We have tried to portray some of the history of the subject and some of its connections with similar devices in mathematics. We…

We present a systematic derivation of some definite integrals in the classical table of Gradshteyn and Ryzhik that can be reduced to the gamma function.

The connection between Lefschetz formulae and zeta function is explained. As a particular example the theory of the generalized Selberg zeta function is presented. Applications are given to the theory of Anosov flows and prime geodesic…

Previously the authors proved subconvexity of Shintani's zeta function enumerating class numbers of binary cubic forms. Here we return to prove subconvexity of the Maass form twisted version.

We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.

The purpose of this paper is to prove that the so-called Quasi-Riemann Hypothesis for the Zeta-function implies the Riemann Hypothesis

These notes give a basic introduction to the theory of $p$-adic and motivic zeta functions, motivic integration, and the monodromy conjecture.

In this paper a double integral containing two Gaussian hypergeometric functions is discussed. The integral is not found in the literature and a direct computation is not (yet) possible. Therefore, a complete different integral is computed…

We prove three theorems on finite real multiple zeta values: the symmetric formula, the sum formula and the height-one duality theorem. These are analogues of their counterparts on finite multiple zeta values.

We show how the formulas in paper Variae considerationes circa series hypergeometricas written by Euler imply the duplication formula for the Gamma-function. This paper can be seen as an Addendum to a previous paper by the author.

This paper shows the Fermi-Dirac Integrals expressed in terms of Riemann and Hurwitz Zeta functions. This is done by defining an auxiliar function that permits rewrite the Fermi-Dirac integral in terms of simpler and known integrals…

In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals

We propose a relation between values of the Riemann zeta function $\zeta$ and a family of integrals. This results in an integral representation for $\zeta(2p)$, where $p$ is a positive integer, and an expression of $\zeta(2p+1)$ involving…

In this paper, we study the relation between the zeta function of a Calabi-Yau hypersurface and the zeta function of its mirror. Two types of arithmetic relations are discovered. This motivates us to formulate two general arithmetic mirror…

The aim of this paper is to derive a summation formula for the alternating infinite series and an expression for zeta function by using hyperbolic secant random variables. These identities involve Euler numbers and are obtained by computing…