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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)].
11L07 Estimates on exponential sums
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[1] Fouvry, E., Iwaniec, H., Exponential sums with monomials. J. Number Theory33 (1989), 311-333. · Zbl 0687.10028
[2] Graham, S.W., Kolesnik, G., Van der Corput’s method of exponential sums. 126, Cambridge University Press, 1991. · Zbl 0713.11001
[3] Heath-Brown, D.R., Weyl’s inequality, Hua’s inequality, and Waring’s problem. J. London Math. Soc.28 (1988), 216-230. · Zbl 0619.10046
[4] Huxley, M.N., Expoential sums and the Riemann zeta function IV. Proc. London Math. Soc66 (1993), 1-40. · Zbl 0803.11046
[5] Huxley, M.N., Area, lattice points and exponential sums. Clarendon Press, Oxford, 1996. · Zbl 0861.11002
[6] Montgomery, H.L., Ten problems on the interface between analytic number theory and harmonic analysis. CBMS 84, American Math. Soc., 1994. · Zbl 0814.11001
[7] Redouaby, M., Sargos, P., Sur la transformation B de Van der Corput. Expo. Math.17 (1999), 207-232 · Zbl 0969.11028
[8] Sargos, P., Un critère de la dérivée cinquième pour les sommes d’exponentielles. Bull. London Math. Soc32 (2000), 398-402. · Zbl 1027.11058
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