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ON THE MERTENS CONJECTURE FOR ELLIPTIC CURVES OVER FINITE FIELDS

Published online by Cambridge University Press:  28 February 2013

PETER HUMPHRIES
PETER HUMPHRIES*
Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 08544, USA email peterch@math.princeton.edu
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Abstract

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We introduce an analogue of the Mertens conjecture for elliptic curves over finite fields. Using a result of Waterhouse, we classify the isogeny classes of elliptic curves for which this conjecture holds in terms of the size of the finite field and the trace of the Frobenius endomorphism acting on the curve.

Keywords

Mertens conjectureelliptic curvefinite fieldfunction field
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 1 , February 2014 , pp. 19 - 32
Copyright
©2013 Australian Mathematical Publishing Association Inc. 

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