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

2021/12/08 by D. J. Prabhakaran, Prabhakaran, D. J., N. Jayakumar +3
Mathematics · Social Sciences · #11F20 #11F27 #33C05 #33D10 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Religion and Sociopolitical Dynamics in Nigeria

paper · pdf · doi:10.48550/arxiv.2112.06653

openalex publication_date 2021/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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