Warning: The NCBI web site requires JavaScript to function. more...
Generate a file for use with external citation management software.
Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA.
Recently, Andrews introduced the function s(n) = spt(n) which counts the number of smallest parts among the integer partitions of n. We show that its generating function satisfies an identity analogous to Ramanujan's mock theta identities. As a consequence, we are able to completely determine the parity of s(n). Using another type of identity, one based on Hecke operators, we obtain a complete multiplicative theory for s(n) modulo 3. These congruences confirm unpublished conjectures of Garvan and Sellers. Our methods generalize to all integral moduli.
Your browsing activity is empty.
Activity recording is turned off.
Turn recording back on