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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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 | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [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 (87i:11119)
  • [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 (81d:10029)
  • [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 (58 #16555)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0776182-0
PII: S 0002-9939(1985)0776182-0
Keywords: Exponential sums over primes
Article copyright: © Copyright 1985 American Mathematical Society