Modularity of a Ramanujan-Selberg continued fraction

Yoonjin Lee, Yoon Kyung Park

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We study a Ramanujan-Selberg continued fraction S(τ) by employing the modular function theory. We first find modular equations of S(τ) of level n for every positive integer n by using affine models of modular curves. This is an extension of Baruah-Saikia's results for level n=3, 5 and 7. We further show that the ray class field modulo 4 over an imaginary quadratic field K is obtained by the value of S2(τ), and we prove the integrality of 1/S(τ) to find its class polynomial for K with τ∈K∩H, where H is the complex upper half plane.

Original languageEnglish
Pages (from-to)373-394
Number of pages22
JournalJournal of Mathematical Analysis and Applications
Volume438
Issue number1
DOIs
StatePublished - 1 Jun 2016

Keywords

  • Class field theory
  • Modular function
  • Ramanujan continued fraction

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