Affiliation: University of Illinois
Email: boylan@math.uiuc.edu
Title Of Talk: Arithmetic of the partition function
Abstract: Ramanujan discovered many interesting properties of the partition function. Perhaps the most famous properties are the Ramanujan congruences p(5n+4) equiv 0 mod 5, p(7n+5) equiv 0 mod 7, p(11n+6) equiv 0 mod 11. Since Ramanujan's work, congruences for p(n) have been widely studied. Using the theory of modular forms modulo l, we show that these congruences are the only ones of the form p(ln+a) equiv 0 mod l. As a corollary, we prove many cases of a famous conjecture of Newman on the distribution of values of p(n) among residue classes mod M.
Last update made Thu Nov 11 14:46:03 EST 2004.
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