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On van der Corput’s method for exponential sums. (Sur la méthode de van der Corput pour les sommes d’exponentielles.) (French) Zbl 1042.11050
Van der Corput’s method and the techniques that have developed from it are devoted to obtaining upper bounds for sums of the form $$\sum_{m=M+1}^{2M} e(TF(m/M))$$, where $$e(x)=e^{2\pi i x}$$ and $$F$$ is a real-valued “almost monomial” function with domain $$[1,2]$$. In this paper, the author proves results about the $$A^kBAD$$ process, where $$A$$ and $$B$$ are the classical van der Corput processes and $$D$$ is the double large sieve introduced by E. Fouvry and H. Iwaniec [J. Number Theory 33, No. 3, 311–333 (1989; Zbl 0687.10028)].
##### MSC:
 11L07 Estimates on exponential sums
##### Keywords:
exponential sums; van der Corput’s method
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##### References:
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