Two theta-function identities of level 10

Anuradha, D and Kumar, Srivatsa B R and Udupa, Sayinath (2020) Two theta-function identities of level 10. Advances in Mathematics: Scientific Journal, 9 (7). pp. 4929-4936. ISSN 1857-8365

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Abstract

In this paper, we prove two theta-function identities using modular equation of degree 3. Furthermore, as an application of this we establish combinatorial interpretations of colored partitions. 1. INTRODUCTION Ramanujan’s theta function f(x, y) is defined as f(x, y) := X∞ n=−∞ x n(n+1)/2 y n(n−1)/2 |xy| < 1. The function f(x, y) enjoys the well-known Jacobi’s triple-product identity [5, p. 35] given by f(x, y) = (−x; xy)∞(−y; xy)∞(xy; xy)∞ , where here and throughout the paper, we assume |q| < 1 and employ the standard notation (x; q)∞ := Y∞ n=0 (1 − xqn ).

Item Type: Article
Subjects: Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 30 Oct 2020 05:35
Last Modified: 30 Oct 2020 05:35
URI: http://eprints.manipal.edu/id/eprint/155955

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