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On certain character sums over p ‐adic rings and their L ‐functions
Author(s) -
Blache Régis
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510571
Subject(s) - character (mathematics) , reciprocal , modulo , mathematics , exponential function , prime (order theory) , gauss sum , series (stratigraphy) , prime power , gauss , quadratic gauss sum , power series , power (physics) , rational function , pure mathematics , arithmetic , combinatorics , mathematical analysis , physics , geometry , philosophy , paleontology , linguistics , biology , quantum mechanics
In this paper we present a new method for evaluating exponential sums associated to a restricted power series in one variable modulo p l , a power of a prime. We show that for sufficiently large l , these sums can be expressed in terms of Gauss sums. Moreover, we study the associated L ‐functions; we show that they are rational, then we determine their degrees and the weights as Weil numbers of their reciprocal roots and poles. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)