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2019•TURKISH JOURNAL OF MATHEMATICSOpen access

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

K. R. Vasuki, Anusha THIPPESHA

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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.

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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.

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Available 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.

Key concepts: Ramanujan's sum, Ramanujan theta function, Mathematics, Modular form, Theta function, Ramanujan tau function, Modular design, Mathematical proof

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