Jacobi-Sohncke Type Mixed Modular Equations And Their Applications

Authors

  • M. S. Mahadeva Naika
  • K. Sushan Bairy
  • C. Shivashankar

DOI:

https://doi.org/10.1285/i15900932v36n1p37

Keywords:

Modular equation, Theta-function, continued fraction

Abstract

In this paper, we establish Jacobi-Sohncke type several new mixed modular equations for composite degrees 1, 3, $n$ and $3n$. As an application, we establish the modular relations between the Ramanujan-Selberg continued fractions $H(q),\ H(q^3),\ H(q^n)$ and $H(q^{3n})$ for $n=2,3,4,5,7,9,11$ and also we obtain congruence relations for color overpartitions of $n$ with odd parts.

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Published

20-04-2016

Issue

Volume 36, Issue 1 (2016)

Section

Articoli

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http://creativecommons.org/licenses/by-nc-nd/3.0/it/legalcode