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A continued fraction of order twelve as a modular function

Title
A continued fraction of order twelve as a modular function
Authors
Lee Y.Park Y.K.
Ewha Authors
이윤진박윤경
SCOPUS Author ID
이윤진scopus; 박윤경scopus
Issue Date
2018
Journal Title
Mathematics of Computation
ISSN
0025-5718JCR Link
Citation
Mathematics of Computation vol. 87, no. 312, pp. 2011 - 2036
Keywords
Modular functionRamanujan continued fraction
Publisher
American Mathematical Society
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
We study a continued fraction U(τ) of order twelve using the modular function theory. We obtain the modular equations of U(τ) by computing the affine models of modular curves X(Γ) with Γ = Γ1(12) ∩ Γ0(12n) for any positive integer n; this is a complete extension of the previous result of Mahadeva Naika et al. and Dharmendra et al. to every positive integer n. We point out that we provide an explicit construction method for finding the modular equations of U(τ). We also prove that these modular equations satisfy the Kronecker congruence relations. Furthermore, we show that we can construct the ray class field modulo 12 over imaginary quadratic fields by using U(τ) and the value U(τ) at an imaginary quadratic argument is a unit. In addition, if U(τ) is expressed in terms of radicals, then we can express U(rτ) in terms of radicals for a positive rational number r. © 2017 American Mathematical Society.
DOI
10.1090/mcom/3259
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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