Related papers: On adelic Hurwitz zeta measures

This note contains a short proof of the functional equation for the zeta function.

If $Z(t) = \chi^{-1/2}(1/2+it)\zeta(1/2+it)$ denotes Hardy's function, where $\zeta(s) = \chi(s)\zeta(1-s)$ is the functional equation of the Riemann zeta-function, then it is proved that $$ \int_0^T Z(t)\d t = O_\e(T^{1/4+\e}). $$

Geometric zeta functions of Ihara and Hashimoto are generalized to higher rank. The $p$-adic version of the Patterson conjecture is proven.

In this paper, we give an overview of the various general methods in computing the zeta function of an algebraic variety defined over a finite field, with an emphasis on computing the reduction modulo $p^m$ of the zeta function of a…

We use $L^2$ estimates for the $\bar\partial$ equation to find geometric conditions on discrete interpolating varieties for weighted spaces $A_p(\C)$ of entire functions such that $| f(z)|\le Ae^{Bp(z)}$ for some $A,B>0$. In particular, we…

We found, by Hurwitz's Zeta Function, a new functional equation for Riemann Zeta Function. Considering this equation for $s=2$ and $s=1$, we determine a relation between the values of Riemann zeta Function on positive integers. The Matrix…

In this paper, we study Iwasawa theory for Tate motives over totally real fields. More precisely, we construct a zeta element that interpolates the values of $L$-functions at positive integers over totally real fields under a certain…

Let $A$ be a square complex matrix, $z_1$, ..., $z_{n}\in\mathbb C$ be (possibly repetitive) points of interpolation, $f$ be analytic in a neighborhood of the convex hull of the union of the spectrum of $A$ and the points $z_1$, ...,…

Following our earlier research, we use the method introduced by the author in \cite{prevost1996} named Remainder Pad\'e Approximant in \cite{rivoalprevost}, to construct approximations of the Hurwitz zeta function. We prove that these…

In 2016, the Hurwitz metric was introduced by D. Minda in arbitrary proper subdomains of the complex plane and he proved that this metric coincides with the Poincar\'e's hyperbolic metric when the domains are simply connected. In this…

We present a new expansion of the zeta-function of Riemann. The current formalism -- which combines both the idea of interpolation with constraints and the concept of hypergeometric functions -- can, in a natural way, be generalised within…

The motion in the complex plane of the zeros to various zeta functions is investigated numerically. First the Hurwitz zeta function is considered and an accurate formula for the distribution of its zeros is suggested. Then functions which…

We interpolate cohomology classes attached to families of Hilbert modular forms. Using this we construct a two variable $p$-adic L-function which interpolates one variable $p$-adic L-functions.

Y\i ld\i r\i m obtained an asymptotic formula of the discrete moment of $|\zeta(\frac{1}{2}+it)|$ over the zero of the higher derivatives of Hardy's $Z$-function. We give a generalization of his result on Hardy's $Z$-function.

In this note we study the cotypes of subrings of ${\mathbb Z}[t]/(t^3)$ using $p$-adic integration.

In this paper, we construct certain analogues of the Arakawa-Kaneko zeta functions. We prove functional relations between these functions and the Mordell-Tornheim multiple zeta functions. Furthermore we give some formulas among…

The paper describes a method for calculating values of Riemann's Zeta function within the critical strip 0< {\sigma} <1 and on its boundary. The approach is based on the "Alternating Zeta function" {\eta}(s). The actual Riemann Zeta…

In this article, we present a new linear independence criterion for values of the $p$-adic polygamma functions defined by J.~Diamond. As an application, we obtain the linear independence of some families of values of the $p$-adic Hurwitz…

This paper provides an introduction to Eisenstein measures, a powerful tool for constructing certain $p$-adic $L$-functions. First seen in Serre's realization of $p$-adic Dedekind zeta functions associated to totally real fields, Eisenstein…

We construct and study a certain zeta function which interpolates multi-poly-Bernoulli numbers at non-positive integers and whose values at positive integers are linear combinations of multiple zeta values. This function can be regarded as…