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The Ramanujan Journal

, Volume 36, Issue 3, pp 483–499 | Cite as

On the representation of the number of integral points of an elliptic curve modulo a prime number

  • Michael T. Rassias
Article
  • 141 Downloads

Abstract

In this paper we shall investigate the problem of the representation of the number of integral points of an elliptic curve modulo a prime number p. We present a way of expressing an exponential sum which involves polynomials of third degree, in explicit non-exponential terms. In the process, we prove explicit formulas for the calculation of certain series involving the Riemann zeta function.

Keywords

Elliptic curves Integral points Exponential sums Riemann zeta function 

Mathematics Subject Classification

11L03 11L07 14H52 11M06 11Yxx 11T71 

Notes

Acknowledgements

I would like to thank my Ph.D. advisor Professor E. Kowalski who suggested to me this area of research and for his very useful advice.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsETH-ZürichZürichSwitzerland

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