Arithmetic properties of certain partition functions and modular forms

Abstract

This thesis studies arithmetic properties of regular overpartitions Andrews singular overpartitions overpartitions into odd parts cubic and overcubic partition pairs and Andrews integer partitions with even parts below odd parts We use various dissections of Ramanujan s theta functions to nd in nite families of arithmetic identities and Ramanujan type congruences for regular overpartitions and overpartitions into odd parts We nd certain congruences satis ed by A n for 4 8 an...