The Sylvester Theorem and the Rogers-Ramanujan Identities over Totally Real Number Fields

2023/11/30 by Jang, Se Wook, Kim, Byeong Moon, Kim, Kwang Hoon
#11P84 #11R80 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2311.18514

Abstract

In this paper, we prove two identities on the partition of a totally positive algebraic integer over a totally real number field which are the generalization of the Sylvester Theorem and that of the Rogers-Ramanujan Identities. Additionally, we give an another version of generalized Rogers-Ramanujan Identities.

Related

• The Euler-Glaisher Theorem over Totally Real Number Fields
• Some consequences of Glaisher's map and a generalization of Sylvester's theorem
• IdentityFinder and some new identities of Rogers-Ramanujan type
• Partition identities associated to Rogers-Ramanujan type identities
• Some New Congruences and Partition-Theoretic Interpretations for the Coefficients of Some Rogers-Ramanujan Type Identities