Affordable Access

Publisher Website

On the Total Degree of Certain L-Functions

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
86
Issue
1
Identifiers
DOI: 10.1006/jnth.2000.2556

Abstract

Abstract Assume a polynomial f∈ F q [ x, y] and an additive character ψ of F q are given. From a set of exponential sums defined by f and ψ one can define an L-function L f ( t), which by results of Dwork and Grothedieck is known to be a rational function. In fact, L f ( t) is the Artin L-function associated to ψ and to an Artin–Schreier covering defined from f. In this note we give bounds for the number of poles of L f ( t) and for its total degree (the number of zeros plus the number of poles). Our bounds are given in terms of the Newton polyhedron of f. The bound for the total degree we give improves, for polynomials in two variables, previous bounds of E. Bombieri (1978, Invent. Math. 47, 29–39) and A. Adolphson–S. Sperber (1987, Invent. Math. 88, 555–569).

There are no comments yet on this publication. Be the first to share your thoughts.

Statistics

Seen <100 times
0 Comments

More articles like this

Combining functions for certainty degrees in consu...

on International Journal of Man-M... Jan 01, 1985

Invariant factors of degree matrices and L-functio...

on Finite Fields and Their Applic...
More articles like this..