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Applications des systèmes diophantiens aux sommes d'exponentielles

Abstract : In the current theory of exponential sums, van der Corput's analytic method which provides classical estimates seems to have reached its limits. Vinogradov's method, and more recently Bombieri and Iwaniec's works introduce mean value theorems which are equivalent to diophantine systems. These can be treated independently with appropriate methods ; arithmetical arguments are particularly relevant. In this thesis, we give upper bounds for the number of solutipns of three diophantine systems which are best possible, up to factors of no importance in the applications. These results give rise to new estimates for exponential sums by means of preliminvy analytic transformations which are cqmpletely clifferent in each of the three cases.
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Submitted on : Thursday, March 29, 2018 - 10:39:26 AM
Last modification on : Saturday, October 16, 2021 - 11:18:03 AM

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Olivier Robert. Applications des systèmes diophantiens aux sommes d'exponentielles. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2001. Français. ⟨NNT : 2001NAN10067⟩. ⟨tel-01746514⟩



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