Zeta Functions of Artin - Schreiercurves over Finite Fields

Computing zeta functions of Artin-Schreier curves over finite fields II

Constructions of Non-Abelian Zeta Functions for Curves

In this paper, we initiate a geometrically oriented study of local and global non-abelian zeta functions for curves. This consists of two parts: construction and justification. For the construction, we first use moduli spaces of semi-stable bundles to introduce a new type of zeta functions for curves defined over finite fields. Then, we prove that these new zeta functions are indeed rational an...

Non-Abelian Zeta Functions For Function Fields

In this paper we initiate a geometrically oriented construction of non-abelian zeta functions for curves defined over finite fields. More precisely, we first introduce new yet genuine non-abelian zeta functions for curves defined over finite fields, by a ‘weighted count’ on rational points over the corresponding moduli spaces of semi-stable vector bundles using moduli interpretation of these po...

Zeta functions for two-dimensional shifts of finite type

This work is concerned with zeta functions of two-dimensional shifts of finite type. A two-dimensional zeta function ζ0(s) which generalizes the Artin-Mazur zeta function was given by Lind for Z2-action φ. The n-th order zeta function ζn of φ on Zn×∞, n ≥ 1, is studied first. The trace operator Tn which is the transition matrix for x-periodic patterns of period n with height 2 is rotationally s...

Riemann-Roch Theorem, Stability and New Zeta Functions for Number Fields

In this paper, we introduce new non-abelian zeta functions for number fields and study their basic properties. Recall that for number fields, we have the classical Dedekind zeta functions. These functions are usually called abelian, since, following Artin, they are associated to one dimensional representations of Galois groups; moreover, following Tate and Iwasawa, they may be constructed as in...