Name
Abstract | ||
|---|---|---|
In the study of partition theory and q-series, identities that relate series to infinite products are of great interest (such as the famous Rogers-Ramanujan identities). Using a recent result of Zagier, we obtain an infinite family of such identities that is indexed by the positive integers. For example, if m = 1, then we obtain the classical Eisenstein series identity Σλ≥1 odd (-1)(λ-1)/2qλ/(1-q2λ)=q Πn=1∞ (1-q8n)4/(1-q4n)2 If m = 2 and (·/3;) denotes the usual Legendre symbol modulo 3, then we obtain Σλ ≥1 (λ/3) qλ/(1-q2λ=q Πn=1∞ (1-qn)(1-q6n)6/(1-q2n)2(1-q3n)3 We describe some of the partition theoretic consequences of these identities. In particular, we find simple formulas that solve the well-known problem of counting the number of representations of an integer as a sum of an arbitrary number of triangular numbers. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1006/jcta.2002.3276 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
great interest,famous rogers-ramanujan identity,positive integer,infinite family,partition identity,classical eisenstein series identity,arbitrary number,partition theory,partition theoretic consequence,recent result,triangular number,rogers ramanujan identities,eisenstein series,indexation | Integer,Discrete mathematics,Combinatorics,Infinite product,Modulo,Legendre symbol,Triangular number,Partition (number theory),Eisenstein series,Mathematics | Journal |
Volume | Issue | ISSN |
100 | 1 | Journal of Combinatorial Theory, Series A |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jayce Getz | 1 | 0 | 0.34 |
| Karl Mahlburg | 2 | 13 | 5.84 |