Theta-function identities of level 8 and its application to partitions

Kumar, B. R. Srivatsa; Rajanna, K. R.; Narendra, R.

doi:10.1007/s13370-018-0643-8

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2020

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“…Srivatsa Kumar and Anu Radha [16] have given a proof of few Somos's identities of levels 10. Srivatsa Kumar et al [17,18] have proved theta function identities of level 6 and 8 which are analogous to Ramanujan's theta function identities. Our aim is to prove some of these new theta-function identities of level 6 conjectured by Somos by using modular equation of degree 3 given by Ramanujan and to establish certain partition identities for them.…”

Section: Introductionmentioning

confidence: 97%

Some Somos’s theta function identities of level 6 and application to partitions

Kumar

Sharath²

2020

Publ Inst Math (Belgr)

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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 a 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.

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Section: Introductionmentioning

confidence: 97%