STICKELBERGER SERIES AND IWASAWA MAIN CONJECTURE FOR FUNCTION FIELDS

Let F be a global function field in characteristic p>0. There exists many different types of L-functions that can be associated to F, such as the Artin L-functions, the Goss Zeta function or the p-adic L-functions. In this work i have investigated the correlations between these analytic objects and the Stickelberger series, which is a formal power series whose coefficients lie in a suitable Galois algebra. In the second part of this work i have studied the Iwasawa extension generated by the p-torsion of a Hayes module and i have used the Stickelberger series to prove a "main conjecture" for the p-part of the class group.