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Dergiler / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 1

On a pair of Ramanujan's modular equations and $P$-$Q$ theta functions of level 35

K. R. VASUKI,Anusha T

Sayfa
63–80
DOI
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Abstract

S. Ramanujan recorded several modular equations and $P$-$Q$ theta function identities in his notebooks and lost notebook without recording the proofs. In this paper, we provide an elementary proof of two modular equations and two $P$-$Q$ theta function identities of level 35, which have been proved by B.C. Berndt using the theory of modular forms.