Open AccessTheta function identities of level 6 and their application to partitions
Author(s) -
Srivatsa B R Kumar,
K. R. Rajanna,
R. Narendra
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1911323s
Subject(s) - mathematics , ramanujan's sum , partition (number theory) , theta function , ramanujan theta function , function (biology) , pure mathematics , identity (music) , combinatorics , aesthetics , evolutionary biology , biology , philosophy
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.