Open AccessSome Somos’s theta function identities of level 6 and application to partitions
Author(s) -
B. R. Srivatsa Kumar,
G. Sharath
Publication year - 2020
Publication title -
publications de l'institut mathématique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.246
H-Index - 17
eISSN - 1820-7405
pISSN - 0350-1302
DOI - 10.2298/pim2022137s
Subject(s) - ramanujan's sum , scripting language , theta function , modular design , function (biology) , generating function , ramanujan theta function , mathematics , calculator , pure mathematics , combinatorics , algebra over a field , arithmetic , computer science , programming language , evolutionary biology , biology , operating system
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.