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The level 13 analogue of the Rogers–Ramanujan continued fraction and its modularity

Title
The level 13 analogue of the Rogers–Ramanujan continued fraction and its modularity
Authors
Lee Y.Park Y.K.
Ewha Authors
이윤진박윤경
SCOPUS Author ID
이윤진scopus; 박윤경scopus
Issue Date
2016
Journal Title
Journal of Number Theory
ISSN
0022-314XJCR Link
Citation
vol. 168, pp. 306 - 333
Keywords
Modular functionModular unitRogers–Ramanujan continued fraction
Publisher
Academic Press Inc.
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
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.
DOI
10.1016/j.jnt.2016.04.009
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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