Affiliation: Cal St Hayward
Email: eichhorn@mcs.csuhayward.edu
Title Of Talk: Partition functions do not concentrate too heavily modulo M
Abstract: Combining work of Ahlgren, Nicolas, Ruzsa, Serre, and Sarkozy, we know that p(n) cannot concentrate too heavily in either residue class modulo 2. Berndt, Yee, and Zaharescu gave infinite families of partition functions that share this property. Also, the work of Ahlgren, Boylan, Brunier, and Ono provides a lower bound for how often p(n) fills each residue class modulo any prime P other than 3, which trivially implies that p(n) cannot concentrate too heavily in any single residue class modulo P. In light of this, it is natural to ask whether or not the aforementioned infinite families of partition functions can concentrate in a single residue class modulo any M. In this talk, we explore the answer to that question. A special case of our results will be a theorem about p(n) modulo 3.
Last update made Sat Nov 13 10:06:08 EST 2004.
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