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A level 16 analogue of Ramanujan series for 1/π

Title
A level 16 analogue of Ramanujan series for 1/π
Authors
Lee Y.Park Y.K.
Ewha Authors
이윤진박윤경
SCOPUS Author ID
이윤진scopus; 박윤경scopus
Issue Date
2017
Journal Title
Journal of Mathematical Analysis and Applications
ISSN
0022-247XJCR Link
Citation
vol. 456, no. 1, pp. 177 - 194
Keywords
Modular equationModular functionRamanujan's series for 1/πRay class field
Publisher
Academic Press Inc.
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
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.
DOI
10.1016/j.jmaa.2017.06.082
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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