Somos's theta-function identities of level 10

Authors: BELAKAVADI RADHAKRISHNA SRIVATSA KUMAR, DEVADAS ANU RADHA

Abstract: Somos discovered about 6277 theta-function identities of different levels using a computer and offered no proof for them, and these identities closely resemble Ramanujan's recordings. The purpose of this paper is to prove some of his theta-function identities of level 10 and to establish certain partition identities for them.

Keywords: Theta-functions, modular equations, Dedekind $\eta$-function, colored partitions

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