Calculatingp(n) Modulo Small Primes Using Quadratic Forms

✍ Scribed by Lawrence Sze

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 239 KB
• Volume: 70
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1998.2230

✦ Synopsis

We use a telescoping method suggested by Ono [5] to compute p(n) (mod l) as a weighted sum over l-affine partitions of size n. When l=2, 3, 5, 7, and 11, these sums are neatly described using binary quadratic forms. Moreover, one immediately obtains classical proofs of the Ramanujan congruences (mod 5), 7, and 11.