A level 16 analogue of Ramanujan series for 1/π
- 주제(키워드) Modular equation , Modular function , Ramanujan's series for 1/π , Ray class field
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Academic Press Inc.
- 발행년도 2017
- URI http://www.dcollection.net/handler/ewha/000000146905
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.jmaa.2017.06.082
초록/요약
The modular function h(τ)=q∏n=1∞[Formula presented] is called a level 16 analogue of Ramanujan's series for 1/π. We prove that h(τ) generates the field of modular functions on Γ0(16) and find its modular equation of level n for any positive integer n. Furthermore, we construct the ray class field K(h(τ)) modulo 4 over an imaginary quadratic field K for τ∈K∩H such that Z[4τ] is the integral closure of Z in K, where H is the complex upper half plane. For any τ∈K∩H, it turns out that the value 1/h(τ) is integral, and we can also explicitly evaluate the values of h(τ) if the discriminant of K is divisible by 4. © 2017 Elsevier Inc.
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