First vertices for hyperelliptic curves in characteristic two

Abstract

We study the Newton polygons of numerators of the zeta functions of $2$-rank $0$ hyperelliptic curves in characteristic $2$. We determine their first generic vertex, and their first vertex in some other non generic cases.

10 pages

References in corpus (2)

• Congruences for L-functions of additive exponential sums
• Valuations of exponential sums and Artin-Schreier curves