A level 16 analogue of Ramanujan series for 1/π

Yoonjin Lee, Yoon Kyung Park

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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.

Original languageEnglish
Pages (from-to)177-194
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - 1 Dec 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.


  • Modular equation
  • Modular function
  • Ramanujan's series for 1/π
  • Ray class field


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