M. Somos has conjectured many theta function identities belonging to different levels. He has done so with the use of a computer but has not chosen to validate these identities. We find that the mentioned identities are analogous to those discovered by Srinivasa Ramanujan. The intent to prove some of the identities prepared by Somos concerning theta function identities of a level six and to also establish certain partition-theoretic interpretations of these identities which we have been successfully proved here.
Srinivasa Ramanujan recorded many modular equations in his notebooks, which
are useful in the computation of class invariants, continued fractions and
the values of theta functions. In this paper, we prove some new modular
equations of signature three by using theta function identities of composite
degrees.
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