Generalized Artin'S Conjecture for Primitive Roots and Cyclicity Mod of Elliptic Curves Over Function Fields
Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 167-173
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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.
Clark, David A.; Kuwata, Masato. Generalized Artin'S Conjecture for Primitive Roots and Cyclicity Mod of Elliptic Curves Over Function Fields. Canadian mathematical bulletin, Tome 38 (1995) no. 2, pp. 167-173. doi: 10.4153/CMB-1995-023-2
@article{10_4153_CMB_1995_023_2,
author = {Clark, David A. and Kuwata, Masato},
title = {Generalized {Artin'S} {Conjecture} for {Primitive} {Roots} and {Cyclicity} {Mod} of {Elliptic} {Curves} {Over} {Function} {Fields}},
journal = {Canadian mathematical bulletin},
pages = {167--173},
year = {1995},
volume = {38},
number = {2},
doi = {10.4153/CMB-1995-023-2},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-023-2/}
}
TY - JOUR AU - Clark, David A. AU - Kuwata, Masato TI - Generalized Artin'S Conjecture for Primitive Roots and Cyclicity Mod of Elliptic Curves Over Function Fields JO - Canadian mathematical bulletin PY - 1995 SP - 167 EP - 173 VL - 38 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-023-2/ DO - 10.4153/CMB-1995-023-2 ID - 10_4153_CMB_1995_023_2 ER -
%0 Journal Article %A Clark, David A. %A Kuwata, Masato %T Generalized Artin'S Conjecture for Primitive Roots and Cyclicity Mod of Elliptic Curves Over Function Fields %J Canadian mathematical bulletin %D 1995 %P 167-173 %V 38 %N 2 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1995-023-2/ %R 10.4153/CMB-1995-023-2 %F 10_4153_CMB_1995_023_2
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