Jacobi-Sohncke Type Mixed Modular Equations And Their Applications


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.

DOI Code: 10.1285/i15900932v36n1p37

Keywords: Modular equation; Theta-function; continued fraction

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