On the representation of the number of integral points of an elliptic curve modulo a prime number
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Date
2015-04
Publication Type
Journal Article
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yes
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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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published
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Journal / series
Volume
36 (3)
Pages / Article No.
483 - 499
Publisher
Springer
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Software
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Subject
Elliptic curves; Integral points; Exponential sums; Riemann zeta function
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Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.