On Group Structures Realized by Elliptic Curves over Arbitrary Finite Fields

被引：18

作者：

Banks, William D. ^{[1
]}

Pappalardi, Francesco ^{[2
]}

Shparlinski, Igor E. ^{[3
]}

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Univ Roma Tre, Dipartimento Matemat, I-00146 Rome, Italy

[3] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia

来源：

EXPERIMENTAL MATHEMATICS | 2012年 / 21卷 / 01期

基金：

澳大利亚研究理事会;

关键词：

elliptic curve; finite field; group structure; ERROR TERM;

D O I：

10.1080/10586458.2011.606075

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at most two). We also study various subsets of this collection that correspond to curves over prime fields or to curves with a prescribed torsion. Some of our results are rigorous and are based on recent advances in analytic number theory; some are conditional under certain widely believed conjectures; and others are purely heuristic in nature.

引用

页码：11 / 25

页数：15

共 27 条

[1] Avanzi R., 2005, HDB ELLIPTIC HYPEREL
[2] An improvement for the large sieve for square moduli
Baier, Stephan
Zhao, Liangyi
[J]. JOURNAL OF NUMBER THEORY, 2008, 128 (01) : 154 - 174
[3] Bombieri-Vinogradov type theorems for sparse sets of moduli
Baier, Stephan
Zhao, Liangyi
[J]. ACTA ARITHMETICA, 2006, 125 (02) : 187 - 201
[4] Baker R., 2010, PRIMES ARITHMETIC PR
[5] Bateman P., 1962, MATH COMPUT, V16, P363
[6] Bounds for the solutions of superelliptic equations
Bugeaud, Y
[J]. COMPOSITIO MATHEMATICA, 1997, 107 (02) : 187 - 219
[7] Bugeaud Y., 1996, C R ACAD SCI PARIS 1, V322, P1119
[8] On Group Structures Realized by Elliptic Curves over a Fixed Finite Field
Farashahi, Reza Rezaeian
Shparlinski, Igor E.
[J]. EXPERIMENTAL MATHEMATICS, 2012, 21 (01) : 1 - 10
[9] Granville A., 1995, SCANDANAVIAN ACTUARI, V1, P12
[10] Halberstam H., 1974, Lond. Math. Soc. Monographs

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