Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Let C be a smooth curve over a Galois ring R. Let f be a function over C, and Ψ be an additive character of order p^l over R; in this paper we study the exponential sums associated to f and Ψ over C, and their L-functions. We show the rationality of the L-functions in a more general setting, then in the case of curves we express them as products of L-functions associated to polynomials over the affine line, each factor coming from a singularity of f. Finally we show that in the case of Morse functions (i.e. having only simple singularities), the degree of the L-functions are, up to sign, the same as in the case of finite fields, yielding very similar bounds for exponential sums.
ISSN: 1071-5797

hal-00551470
https://hal.archives-ouvertes.fr/hal-00551470
https://hal.archives-ouvertes.fr/hal-00551470/document
https://hal.archives-ouvertes.fr/hal-00551470/file/Charlefinal.pdf
DOI : 10.1016/j.ffa.2009.01.001