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Exponential sums over primes in an arithmetic progression

Authors: Antal Balog and Alberto Perelli
Journal: Proc. Amer. Math. Soc. 93 (1985), 578-582
MSC: Primary 11L40; Secondary 11L20
MathSciNet review: 776182
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Abstract: In 1979 A. F. Lavrik obtained some estimates for exponential sums over primes in arithmetic progressions by an analytic method. In the present paper we give an estimate for the same sums, comparable with Lavrik's estimate, by means of elementary methods like Vaughan's identity.

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  • [1] Antal Balog, On sums over primes, Elementary and analytic theory of numbers (Warsaw, 1982) Banach Center Publ., vol. 17, PWN, Warsaw, 1985, pp. 9–19. MR 840470
  • [2] A. F. Lavrik, Analytic method of estimates of trigonometric sums by the primes of an arithmetic progression, Dokl. Akad. Nauk SSSR 248 (1979), no. 5, 1059–1063 (Russian). MR 553926
  • [3] R. C. Vaughan, On the estimation of trigonometrical sums over primes, and related questions, Mittag-Leffler Institut Report, no. 9, 1977.
  • [4] Robert-C. Vaughan, Sommes trigonométriques sur les nombres premiers, C. R. Acad. Sci. Paris Sér. A-B 285 (1977), no. 16, A981–A983 (French, with English summary). MR 0498434

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Keywords: Exponential sums over primes
Article copyright: © Copyright 1985 American Mathematical Society

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