Related papers: The cyclotomic trace map and values of zeta-functi…

We classify all cyclotomic matrices over real quadratic integer rings and we show that this classification is the same as classifying cyclotomic matrices over the compositum all real quadratic integer rings. Moreover, we enumerate a related…

We provide a proof of a conjecture by Zhao concerning the structure of certain relations among cyclotomic multiple zeta values in weight two. We formulate this conjecture in a broader algebraic setting in which we give a natural equivalence…

In this paper, we give some explicit evaluations of multiple zeta-star values which are rational multiple of powers of $\pi^2$.

It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the hole complex plane. In this paper, certain cases of specific (non-real analytic) smooth functions…

A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structure, plus countably many special…

We show how regulator constants of a finitely generated $\mathbb{Z}[G]$-module can be related to $G$-cohomology, where $G$ is a finite group. We then derive consequences of such relation for modules naturally arising in number theory, such…

In this manuscript, we investigate some properties of certain counting functions, associated to the ergodic sums computed along the periodic orbits of the skew-product map, related to a finitely generated rational semigroup. To be precise,…

We show that it is possible to approximate the zeta-function of a curve over a finite field by meromorphic functions which satisfy the same functional equation and moreover satisfy (respectively do not satisfy) the analogue of the Riemann…

Some zeta functions which are naturally attached to the locally homogeneous vector bundles over compact locally symmetric spaces of rank one are investigated. We prove that such functions can be expressed in terms of entire functions whose…

A main theme of the paper is a conjecture of Bloch-Kato on the image of $p$-adic regulator maps for a proper smooth variety $X$ over an algebraic number field $k$. The conjecture for a regulator map of particular degree and weight is…

We use partial zeta functions to analyse the asymptotic behaviour of certain smooth arithmetical sums over smooth k-free integers.

We show that the motivic zeta functions of smooth, geometrically connected curves with no rational points are rational functions. This was previously known only for curves whose smooth projective models have a rational point on each…

Let X be a regular scheme, projective and flat over Spec \mathbb Z. We give a conjectural formula, up to sign and powers of 2, for \zeta^*(X,r), the leading term in the series expansion of \zeta(X,s) at s=r, in terms of Weil-etale motivic…

Given a smooth variety $X$ and a regular function $f$ on it, by considering the dlt modification, we define the dlt motivic zeta function $Z^{\rm dlt}_{\rm mot}(s)$ which does not depend on the choice of the dlt modification.

We introduce a cohomology theory for a class of projective varieties over a finite field coming from the canonical trace on a C*-algebra attached to the variety. Using the cohomology, we prove the rationality, functional equation and the…

Slice-regular functions of a quaternionic variable have been studied extensively in the last 12 years, resulting, in many ways, quite close to classical holomorphic functions of a complex variable; indeed, there is a correspondence between…

In this work we study the Artin-Mazur zeta function for piecewise monotone functions acting on a compact interval of real numbers. In the case of unimodal maps, Milnor and Thurston gave a characterization for the rationality of the…

We study the rationality of the Artin-Mazur zeta function of a dynamical system defined by a polynomial self-map of A^1(k), where k is the algebraic closure of the finite field F_p. The zeta functions of the maps f(x)=x^m for (p,m)=1 and…

Let X be a projective scheme over a finite field. In this paper, we consider the asymptotic behavior of the number of effective cycles on X with bounded degree as it goes to the infinity. By this estimate, we can define a certain kind of…

In this paper, we study the Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds. These zeta functions are defined on one complex variable $s$ in some right half-plane of $\mathbb{C}$. We use the Selberg trace…