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On the Distribution of Supersingular Primes

Published online by Cambridge University Press:  20 November 2018

Etienne Fouvry  and
M. Ram Murty
Etienne Fouvry
Affiliation:
Mathématique- Bâtiment 425 Université de Paris-Sud F-91405 Orsay Cedex France
M. Ram Murty
Affiliation:
Department of Mathematics McGill University Montreal, Quebec H3A 2K6
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Abstract

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Let E be a fixed elliptic curve defined over the rational numbers. We prove that the number of primes p ≤ x such that E has supersingular reduction mod p is greater than for any positive δ and x sufficiently large. Here logkx is defined recursively as log(logk-1 x) and log1x = logx. We also establish several results related to the Lang-Trotter conjecture.

Keywords

11G0511N36
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 1 , 01 February 1996 , pp. 81 - 104
Copyright
Copyright © Canadian Mathematical Society 1997

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