A Note on Somos’s Identities of Level 6

Radha, Anu D and Kumar, Srivatsa B R and Udupa, Sayinath (2022) A Note on Somos’s Identities of Level 6. IAENG International Journal of Applied Mathematics, 52 (2). ISSN 1992-9978

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Abstract

Michael Somos conjectured thousands of theta-functions of various levels with the help of computer and not provided the proof. These theta-functions highly matches Ramanujan’s recordings. The objective of our work in this paper is to prove two theta-functions of level 6 conjectured by Somos and to give an alternate proof of the identities proved by B. R. Srivatsa Kumar and G. Sharath. Further, as an application of this, we offer colored partition identities for the same.

Item Type: Article
Uncontrolled Keywords: Colored partitions, Dedekind eta-function, Modular equations, Theta functions.
Subjects: Engineering > MIT Manipal > Mathematics
Depositing User: MIT Library
Date Deposited: 27 Jul 2022 09:23
Last Modified: 27 Jul 2022 09:23
URI: http://eprints.manipal.edu/id/eprint/159045

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