Elliptic curves with no exceptional primes

被引：55
作者：
Duke, W
机构：
来源：
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE | 1997年 / 325卷 / 08期
关键词：
D O I：
10.1016/S0764-4442(97)80118-8
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let E be an elliptic curve over Q. A prime N is said to be exceptional for E if the mod N Galois representation of E is not surjective, i.e. if the Galois group of the N-th division field of E is not equal to GL (2, N). We show that, in terms of heights, almost all curves have no exceptional prime.
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页码：813 / 818
页数：6
相关论文
共 16 条
[1]  
ARTIN E, 1923, HAMBURFER ABH, V89, P105
[2]   THE AVERAGE RANK OF ELLIPTIC-CURVES .1. [J].
BRUMER, A .
INVENTIONES MATHEMATICAE, 1992, 109 (03) :445-472
[3]  
COX DA, 1989, PRIMES FORM X2 PLUS
[4]  
Davenport H., 1980, MULTIPLICATIVE NUMBE
[5]  
DEURING M, 1941, HAMBURFER ABH, P197
[6]  
Eichler M., 1954, Arch. Math., V5, P355
[7]  
GALLAGHER PX, 1972, P S PURE MATH, V24, P91
[8]  
HURWITZ A, 1985, WERKE BD, V2, P51
[9]   LARGE SIEVE INEQUALITY FOR ALGEBRAIC NUMBER FIELDS [J].
HUXLEY, MN .
MATHEMATIKA, 1968, 15 (30P2) :178-&
[10]   GALOIS PROPERTIES OF DIVISION-FIELDS OF ELLIPTIC-CURVES [J].
MASSER, DW ;
WUSTHOLZ, G .
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1993, 25 :247-254
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