Theta Function Identities of Level $6$ and their Application to Partitions

Abstract

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.