The level 13 analogue of the Rogers–Ramanujan continued fraction and its modularity
- 주제(키워드) Modular function , Modular unit , Rogers–Ramanujan continued fraction
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Academic Press Inc.
- 발행년도 2016
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000135429
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.jnt.2016.04.009
초록/요약
We prove the modularity of the level 13 analogue r13(τ) of the Rogers–Ramanujan continued fraction. We establish some properties of r13(τ) using the modular function theory. We first prove that r13(τ) is a generator of the function field on Γ0(13). We then find modular equations of r13(τ) of level n for every positive integer n by using affine models of modular curves; this is an extension of Cooper and Ye's results with levels n=2,3 and 7 to every level n. We further show that the value r13(τ) is an algebraic unit for any τ∈K−Q, where K is an imaginary quadratic field. © 2016 Elsevier Inc.
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