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On the Total Degree of Certain L-Functions

✍ Scribed by Ricardo Garcı́a López

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
102 KB
Volume
86
Category
Article
ISSN
0022-314X

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✦ Synopsis

Assume a polynomial f # F q [x, y] and an additive character of F q are given. From a set of exponential sums defined by f and 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 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

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