Acta Math Vietnam (2016) 41:633–660 DOI 10.1007/s40306-016-0170-3 Color Partition Identities Arising from Ramanujan’s Theta-Functions M. S. Mahadeva Naika 1 · B. Hemanthkumar 1 · H. S. Sumanth Bharadwaj 1 Received: 29 January 2015 / Revised: 28 June 2015 / Accepted: 6 July 2015 / © Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016 Abstract We establish several partition identities with distinct colors that arise from Ramanujan’s theta-function identities and formulas for multipliers in the theory of modu- lar equations. Also, we deduce few partition congruences as a corollary of some partition identities. Keywords Color partition identities · Theta–functions · Partition congruences · Modular equations Mathematics Subject Classification (2010) 11P83 · 05A17 1 Introduction In [12], H. M. Farkas and I. Kra observed that certain theta constant identities can be inter- preted into partition identities. The following theorem is the most elegant of their three partition theorems. Theorem 1.1 Let S denote the set consisting of one copy of the positive integers and one additional copy of those positive integers that are multiples of 7. Then for each positive  M. S. Mahadeva Naika msmnaika@rediffmail.com B. Hemanthkumar hemanthkumarb.30@gmail.com H. S. Sumanth Bharadwaj sumanthbharadwaj@gmail.com 1 Department of Mathematics, Bangalore University, Central College Campus, Bengaluru 560 001, Karnataka, India Published online: 18 February 2016