ALGEBRAIC DIVISIBILITY SEQUENCES OVER FUNCTION FIELDS

被引：9

作者：

Ingram, Patrick ^{[2
]}

Mahe, Valery ^{[3
]}

Silverman, Joseph H. ^{[1
]}

Stange, Katherine E. ^{[4
]}

Streng, Marco ^{[5
]}

机构：

[1] Brown Univ, Dept Math, Providence, RI 02912 USA

[2] Colorado State Univ, Dept Math, Ft Collins, CO 80521 USA

[3] Ecole Polytech Fed Lausanne, SB IMB CSAG, CH-1015 Lausanne, Switzerland

[4] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[5] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2012年 / 92卷 / 01期

基金：

英国工程与自然科学研究理事会; 加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

lucas sequence; elliptic divisibility sequence; primitive divisor; function field over number field; HILBERTS 10TH PROBLEM; ELLIPTIC-CURVES; PRIMITIVE DIVISORS; NUMBER-FIELDS; CANONICAL HEIGHT; INTEGRAL POINTS; WEIL HEIGHT; CONJECTURE; LUCAS; DIFFERENCE;

D O I：

10.1017/S1446788712000092

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we study the existence of primes and of primitive divisors in function field analogues of classical divisibility sequences. Under various hypotheses, we prove that Lucas sequences and elliptic divisibility sequences over function fields defined over number fields contain infinitely many irreducible elements. We also prove that an elliptic divisibility sequence over a function field has only finitely many terms lacking a primitive divisor.

引用

页码：99 / 126

页数：28

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