Some Somos's Theta Function Identities of Level 6 and Application to Partitions

Belakavadi Radhakrishna Srivatsa Kumar, Gururaj Sharath

M.~Somos discovered around 6200 theta function identities using PARI/GP scripts without offering the proof. He runs PARI/GP scripts and it works as a sophisticated programmable calculator. These identities highly resemble those of Ramanujan's identities. Here we prove few theta-function identities of level 6 discovered by Somos by using modular equations of degree 3 given by Ramanujan and further we extract some interesting combinatorial interpretations of colored partitions.