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Generalized Artin'S Conjecture for Primitive Roots and Cyclicity Mod of Elliptic Curves Over Function Fields

Published online by Cambridge University Press:  20 November 2018

David A. Clark  and
Masato Kuwata
David A. Clark
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montréal, Québec H3A 2K6
Masato Kuwata
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. West, Montréal, Québec H3A 2K6
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Abstract

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Let k = Fq be a finite field of characteristic p with q elements and let K be a function field of one variable over k. Consider an elliptic curve E defined over K. We determine how often the reduction of this elliptic curve to a prime ideal is cyclic. This is done by generalizing a result of Bilharz to a more general form of Artin's primitive roots problem formulated by R. Murty.

Keywords

11R5811G05elliptic curvesfunction fields
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 167 - 173
Copyright
Copyright © Canadian Mathematical Society 1995

References

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