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.
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Notes
By f′(x) we denote the derivative df(x)/dx.
By r′ we denote the derivative dr(x,p)/dx.
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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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Rassias, M.T. On the representation of the number of integral points of an elliptic curve modulo a prime number. Ramanujan J 36, 483–499 (2015). https://doi.org/10.1007/s11139-013-9524-9
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DOI: https://doi.org/10.1007/s11139-013-9524-9