Modularity of a Ramanujan-Selberg continued fraction
- 주제(키워드) Class field theory , Modular function , Ramanujan continued fraction
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Academic Press Inc.
- 발행년도 2016
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000125440
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.jmaa.2016.01.065
초록/요약
We study a Ramanujan-Selberg continued fraction S(τ) by employing the modular function theory. We first find modular equations of S(τ) of level n for every positive integer n by using affine models of modular curves. This is an extension of Baruah-Saikia's results for level n=3, 5 and 7. We further show that the ray class field modulo 4 over an imaginary quadratic field K is obtained by the value of S2(τ), and we prove the integrality of 1/S(τ) to find its class polynomial for K with τ∈K∩H, where H is the complex upper half plane. © 2016 Elsevier Inc.
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