✦ LIBER ✦

A Note on Zeta Measures over Function Fields

✍ Scribed by Zifeng Yang

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 206 KB
Volume: 90
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2597

No coin nor oath required. For personal study only.

✦ Synopsis

Let r be a power of a prime number p, F r be the finite field of r elements, and F r [T] be the polynomial ring over F r . As an analogue to the Riemann zeta function over Z, Goss constructed the zeta function Fr [T] (s) over F r [T]. In order to study this zeta function, Thakur calculated the divided power series associated to the zeta measure + x on F r [T] v , where v is a finite place of F r (T ). This paper calculates the divided power series associated to the zeta measure on F r [T] =F r [[ 1T ]] and expresses Fr [T] (s) by an integral of some locally analytic function.

📜 SIMILAR VOLUMES

Selberg Zeta Functions over Function Fie

Selberg Zeta Functions over Function Fields

✍ Hirofumi Nagoshi 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 236 KB

We compute explicitly the Selberg trace formula for principal congruence subgroups of PGL(2, F q [t]) which is the modular group in positive characteristic cases. We also express the Selberg zeta function as a determinant of the Laplacian which is composed of both discrete and continuous spectra. Al

A Note on the Zeta Function of a Graph

✍ Sam Northshield 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 113 KB

The number of spanning trees in a finite graph is first expressed as the derivative (at 1) of a determinant and then in terms of a zeta function. This generalizes a result of Hashimoto to non-regular graphs. ## 1998 Academic Press Let G be a finite graph. The complexity of G, denoted }, is the num

Partial Zeta Functions of Algebraic Vari

Partial Zeta Functions of Algebraic Varieties over Finite Fields

✍ Daqing Wan 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 147 KB

## DEDICATED TO PROFESSOR CHAO KO ON THE OCCASION OF HIS 90TH BIRTHDAY Motivated by arithmetic applications, we introduce the notion of a partial zeta function which generalizes the classical zeta function of an algebraic variety de"ned over a "nite "eld. We then explain two approaches to the gene

On Class Number Relations over Function

On Class Number Relations over Function Fields

✍ Julie T.-Y Wang; Jing Yu 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 263 KB

The analogues of the classical Kronecker and Hurwitz class number relations for function fields of any positive characteristic are obtained by a method parallel to the classical proof. In the case of even characteristic, purely inseparable orders also have to be taken into account. A subtle point is

On Artin′s Conjecture over Function Fiel

On Artin′s Conjecture over Function Fields

✍ F. Pappalardi; I. Shparlinski 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 160 KB

We prove an unconditional analog of Artin's conjecture for the function field of a curve over a finite field. 1 teys Acadumic Press. fnc.

A Note on Tamely Ramified Towers of Glob

A Note on Tamely Ramified Towers of Global Function Fields

✍ Bruno Angles; Christian Maire 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 103 KB

By using rami"ed Hilbert Class Field Towers we improve lower asymptotic bounds of the number of rational points of smooth algebraic curves over % and % . ## 2002 Elsevier Science (USA)