Let be an elliptic curve defined over a number field, and let be a point of infinite order. It is natural to ask how many integers fail to occur as the order of modulo a prime of . For , a quadratic twist of , and as above, we show that there is at most one such .
Soient une courbe elliptique définie sur un corps de nombres et un point d’ordre infini. Il est naturel de se demander combien de nombres entiers n’apparaissent pas comme ordre du point modulo un idéal premier de . Dans le cas où , une tordue quadratique de et comme ci-dessus, nous démontrons qu’il existe au plus un tel .
@article{JTNB_2009__21_3_609_0, author = {Ingram, Patrick}, title = {A quantitative primitive divisor result for points on elliptic curves}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {609--634}, publisher = {Universit\'e Bordeaux 1}, volume = {21}, number = {3}, year = {2009}, doi = {10.5802/jtnb.691}, zbl = {1208.11073}, mrnumber = {2605536}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.691/} }
TY - JOUR AU - Ingram, Patrick TI - A quantitative primitive divisor result for points on elliptic curves JO - Journal de théorie des nombres de Bordeaux PY - 2009 SP - 609 EP - 634 VL - 21 IS - 3 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.691/ DO - 10.5802/jtnb.691 LA - en ID - JTNB_2009__21_3_609_0 ER -
%0 Journal Article %A Ingram, Patrick %T A quantitative primitive divisor result for points on elliptic curves %J Journal de théorie des nombres de Bordeaux %D 2009 %P 609-634 %V 21 %N 3 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.691/ %R 10.5802/jtnb.691 %G en %F JTNB_2009__21_3_609_0
Ingram, Patrick. A quantitative primitive divisor result for points on elliptic curves. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, pp. 609-634. doi : 10.5802/jtnb.691. http://archive.numdam.org/articles/10.5802/jtnb.691/
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