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The geometry of the third moment of exponential sums
Langue
en
Article de revue
Ce document a été publié dans
Journal de Théorie des Nombres de Bordeaux. 2009-05-01, vol. Volume en l'honneur de Henri Cohen, p. ?
Société Arithmétique de Bordeaux
Résumé en anglais
We give a geometric interpretation (and we deduce an explicit formula) for two types of exponential sums, one of which is the third moment of certain Kloosterman sums. We establish a connection between the sums considered ...Lire la suite >
We give a geometric interpretation (and we deduce an explicit formula) for two types of exponential sums, one of which is the third moment of certain Kloosterman sums. We establish a connection between the sums considered and the number of rational points over finite fields on explicit smooth projective surfaces, one of which is a K3 surface, whereas the other is a smooth cubic surface. As a consequence, we obtain, applying Grothendieck-Lefschetz theory, a generalized formula for the third moment of Kloosterman sums first investigated by D. H. and E. Lehmer in the 60's .< Réduire
Origine
Importé de halUnités de recherche