ON ASYMPTOTICALLY OPTIMAL TOWERS OVER QUADRATIC FIELDS RELATED TO GAUSS HYPERGEOMETRIC FUNCTIONS

被引：5
|
作者：
Hasegawa, Takehiro [1 ]
机构：
[1] Waseda Univ, Sch Educ, Dept Math, Tokyo 1698050, Japan
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2010年 / 6卷 / 05期
关键词：
Towers of function fields; rational points; finite fields; hypergeometric functions; Deuring's polynomial; ALGEBRAIC-GEOMETRIC CODES; FINITE-FIELDS; TAME TOWERS; DIFFERENTIAL-EQUATIONS; ELLIPTIC-CURVES; CONSTRUCTION; INVARIANTS; ALGORITHM; SEQUENCE;
D O I：
10.1142/S1793042110003344
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We define two asymptotically optimal towers over quadratic fields, and give the explicit descriptions of the ramification loci and the sets of places splitting completely, which relate to the elliptic modular curves X(0)(4(n)) and X(0)(3(n)), respectively. Moreover, in the last section, we determine completely the modularity of a tower given by Maharaj and Wulftange in [18].
引用
收藏
页码：989 / 1009
页数：21
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