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Some applications of eta-quotients

Part of: Algebraic number theory: global fields Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  22 March 2016

Ick Sun Eum ,
Ja Kyung Koo  and
Dong Hwa Shin
Ick Sun Eum
Affiliation:
School of Mathematics, Korea Institute For Advanced Study, Seoul 02455, Republic of Korea (zandc@kias.re.kr)
Ja Kyung Koo
Affiliation:
Department of Mathematical Sciences, KAIST, Daejeon 34141, Republic of Korea (jkkoo@math.kaist.ac.kr)
Dong Hwa Shin*
Affiliation:
Department of Mathematics, Hankuk University of Foreign Studies, Yongin-si, Gyeonggi-do 17035, Republic of Korea (dhshin@hufs.ac.kr)
*
*Corresponding author.
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Extract

We show that every modular form on Γ0(2n) (n ⩾ 2) can be expressed as a sum of eta-quotients, which is a partial answer to Ono's problem. Furthermore, we construct a primitive generator of the ring class field of the order of conductor 4N (N ⩾ 1) in an imaginary quadratic field in terms of the special value of a certain eta-quotient.

Keywords

eta-quotientsmodular formsring class fields

MSC classification

Secondary: 11F20: Dedekind eta function, Dedekind sums 11F11: Holomorphic modular forms of integral weight 11R37: Class field theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 3 , June 2016 , pp. 565 - 578
Copyright
Copyright © Royal Society of Edinburgh 2016 

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