Let be the cyclic group of order , a divisor of and a divisor of . We introduce the set of -free elements of and derive a lower bound for the number of elements for which is -free and is -free, where . As an application, we consider the existence of -primitive points on curves like and find, in particular, all the odd prime powers for which the elliptic curves contain an -primitive point.
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Accepted:
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DOI: 10.5802/crmath.328
Keywords: finite fields, character sums, elliptic curves
Stephen D. Cohen 1; Giorgos Kapetanakis 2; Lucas Reis 3
@article{CRMATH_2022__360_G6_641_0, author = {Stephen D. Cohen and Giorgos Kapetanakis and Lucas Reis}, title = {The existence of $\protect \mathbb{F}_q$-primitive points on curves using freeness}, journal = {Comptes Rendus. Math\'ematique}, pages = {641--652}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, year = {2022}, doi = {10.5802/crmath.328}, zbl = {07547263}, language = {en}, }
TY - JOUR AU - Stephen D. Cohen AU - Giorgos Kapetanakis AU - Lucas Reis TI - The existence of $\protect \mathbb{F}_q$-primitive points on curves using freeness JO - Comptes Rendus. Mathématique PY - 2022 SP - 641 EP - 652 VL - 360 PB - Académie des sciences, Paris DO - 10.5802/crmath.328 LA - en ID - CRMATH_2022__360_G6_641_0 ER -
%0 Journal Article %A Stephen D. Cohen %A Giorgos Kapetanakis %A Lucas Reis %T The existence of $\protect \mathbb{F}_q$-primitive points on curves using freeness %J Comptes Rendus. Mathématique %D 2022 %P 641-652 %V 360 %I Académie des sciences, Paris %R 10.5802/crmath.328 %G en %F CRMATH_2022__360_G6_641_0
Stephen D. Cohen; Giorgos Kapetanakis; Lucas Reis. The existence of $\protect \mathbb{F}_q$-primitive points on curves using freeness. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 641-652. doi : 10.5802/crmath.328. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.328/
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