Generalized class invariants with 'Thetanullwerte'

被引：1

作者：

Uzunkol, Osmanbey ^{[1
]}

机构：

[1] Carl von Ossietzky Univ Oldenburg, Inst Math, D-26111 Oldenburg, Germany

来源：

TURKISH JOURNAL OF MATHEMATICS | 2013年 / 37卷 / 01期

关键词：

Class polynomials; theta functions; complex multiplication; CLASS POLYNOMIALS;

D O I：

10.3906/mat-1106-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce generalized class invariants as quotients of Thetanullwerte, which realize the computation of class polynomials more efficiently than as quotients of values of the Dedekind eta-function. Furthermore, we prove that these invariants are units in the corresponding class field as most of their classical counterparts.

引用

页码：165 / 181

页数：17

共 18 条

[1] [Anonymous], 1974, Theta functions with applications to Riemann surfaces
[2] [Anonymous], 1973, Elliptic Functions
[3] Belding J, 2008, LECT NOTES COMPUT SC, V5011, P282, DOI 10.1007/978-3-540-79456-1_19
[4] ON THE ZETA-FUNCTIONS OF ALGEBRAIC NUMBER FIELDS
BRAUER, R
[J]. AMERICAN JOURNAL OF MATHEMATICS, 1947, 69 (02) : 243 - 250
[5] Deuring M., 1958, ENZYKL MATH WISS, V2
[6] Dupont R., 2006, THESIS ECOLE POLYTEC
[7] FAST EVALUATION OF MODULAR FUNCTIONS USING NEWTON ITERATIONS AND THE AGM
Dupont, Regis
[J]. MATHEMATICS OF COMPUTATION, 2011, 80 (275) : 1823 - 1847
[8] Enge A., 2009, PREPRINT
[9] Gee A., 2001, THESIS U LEIDEN
[10] Schlafli modular equations for generalized Weber functions
Hart, William B.
[J]. RAMANUJAN JOURNAL, 2008, 15 (03) : 435 - 468

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