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arXiv · 2112.06653

Ramanujan's type of product of theta functions and its applications

D. J. Prabhakaran·N. Jayakumar·K. Ranjithkumar
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Abstract

In this paper, we initiate a generous amount of new-found general theorems for explicit evaluations of product of the theta functions $b_{m, n}$ using Kronecker's limit formula and other various novel explicit evaluations that were introduced thereupon. Also, we have obtained a few novel values of Ramanujan's class invariant $g_n$ using new-found values of $b_{m, n}$. Eventually, we have shown that $b_{m, n}$ is the unit in certain algebraic number fields.

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D. J. Prabhakaran, N. Jayakumar, K. Ranjithkumar. 2021-12-08. Ramanujan's type of product of theta functions and its applications. https://arxiv.org/abs/2112.06653

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