On certain character sums over p ‐adic rings and their L ‐functions |
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| Authors: | Régis Blache |
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| Institution: | Equipe “Géométrie Algébrique et Applications à la Théorie de l'Information”, Université de Polynésie Fran?aise, BP 6570, 98702 Faa'a, Tahiti, Polynésie Fran?aisePhone: +689 803 824, Fax: +689 803 804 |
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| Abstract: | In this paper we present a new method for evaluating exponential sums associated to a restricted power series in one variable modulo pl , 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) |
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| Keywords: | p ‐adic character sums L ‐functions Gauss sums Weil numbers |
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