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Sur la méthode de Van der Corput pour les sommes d'exponentielles

Abstract : In modern methods for analytic exponential sums theory, the A and B Van der Corput's process occur in various forms where more accuracy is needed. The first part of this thesis achieves a complete study of B process for single exponential sums or sums with a parameter. In the second part, Fouvry and Iwaniec's method for multiple exponential sums with monomial is combined with A and B Vander Corput's process to get new bounds for single exponential sums which complete Huxley's table. The third part gives an accurate estimation for single oscillating integrals when the critical point is close to the endpoints of the integration interval which applies to mean values of oscillating integrals such as those that occur in the study of multiple B transform.
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Submitted on : Thursday, March 29, 2018 - 10:50:53 AM
Last modification on : Thursday, January 21, 2021 - 3:05:15 PM


  • HAL Id : tel-01747094, version 1



Marouan Redouaby. Sur la méthode de Van der Corput pour les sommes d'exponentielles. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 1999. Français. ⟨NNT : 1999NAN10224⟩. ⟨tel-01747094⟩



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