Primitive and totally primitive Fricke families with applications (II)

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Jung, Ho Yun¹  Koo, Ja Kyung²  Shin, Dong Hwa³ 

[1] Sungkyunkwan Univ, Appl Algebra & Optimizat Res Ctr, Suwon 16419, Gyeonggi Do, South Korea

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon 34141, South Korea

[3] Hankuk Univ Foreign Studies, Dept Math, Yongin 17035, Gyeonggi Do, South Korea

关键词: Fricke families;    Modular functions;   

DOI  :  10.1016/j.jmaa.2018.11.033

来源: Elsevier

【 摘 要 】

We find necessary and sufficient conditions for a Fricke family of level N (>= 2) to be primitive or totally primitive. Let K be an imaginary quadratic field of discriminant d(kappa) other than Q(root-7) and Q(root-3). As applications of Fricke families, we show that if vertical bar d(kappa)vertical bar is sufficiently large, then the special values of a primitive Fricke family generate the ray class field K(N) modulo N over K. Moreover, we construct a primitive generator of K(N) over K in terms of the special values of classical Fricke functions for every K which would be a partial answer to a question of Hasse and Ramachandra. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free