کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4594810 1335783 2009 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Arithmetic of the Ramanujan–Göllnitz–Gordon continued fraction
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Arithmetic of the Ramanujan–Göllnitz–Gordon continued fraction
چکیده انگلیسی

TextWe extend the results of Chan and Huang [H.H. Chan, S.-S. Huang, On the Ramanujan–Göllnitz–Gordon continued fraction, Ramanujan J. 1 (1997) 75–90] and Vasuki, Srivatsa Kumar [K.R. Vasuki, B.R. Srivatsa Kumar, Certain identities for Ramanujan–Göllnitz–Gordon continued fraction, J. Comput. Appl. Math. 187 (2006) 87–95] to all odd primes p   on the modular equations of the Ramanujan–Göllnitz–Gordon continued fraction v(τ)v(τ) by computing the affine models of modular curves X(Γ)X(Γ) with Γ=Γ1(8)∩Γ0(16p)Γ=Γ1(8)∩Γ0(16p). We then deduce the Kronecker congruence relations for these modular equations. Further, by showing that v(τ)v(τ) is a modular unit over ZZ we give a new proof of the fact that the singular values of v(τ)v(τ) are units at all imaginary quadratic arguments and obtain that they generate ray class fields modulo 8 over imaginary quadratic fields.VideoFor a video summary of this paper, please visit http://www.youtube.com/watch?v=FWdmYvdf5Jg.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 129, Issue 4, April 2009, Pages 922–947
نویسندگان
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