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An Arithmetical Function Associated With the Rank of Elliptic Curves

Published online by Cambridge University Press:  20 November 2018

David Clark
David Clark*
Affiliation:
Department of Mathematics and Statistics McGill University Montréal, Quebec, H3A 2K6
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Abstract

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We define an arithmetical function, f(n), which gives a lower bound for the rank of elliptic curves, y2 = x3 + nx, n square-free. Thus, if f(n) is unbounded for square-free values of n, then there are elliptic curves of arbitrarily large rank. We show that f(n) is unbounded as n ranges over all integers.

Keywords

11G0511D85.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 2 , 01 June 1991 , pp. 181 - 185
Copyright
Copyright © Canadian Mathematical Society 1991

References

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