Congruence Properties Of Some Partition Functions

This thesis first gives the congruence properties of the coefficients of a sixth order mock theta function,and then systematically investigates some infinite families of congruence properties of overpartitions.The main work is as follows.Chapter 1,gives the research background of the partition function,the research progress of the two partition functions related to this thesis,and the main work of this thesis.Chapter 2,investigates the arithmetic properties for the coefficients of a sixth order mock theta function ?(q)given by McIntosh.This chapter first apply the dis-section method to give the corresponding generating function of the coefficients of the?(q),and then use the elementary method and the modular form method to prove some congruences of the coefficients of the ?(q)respectively.The work of this chapter enriches the examples of the Ramanujan-type congruences of the mock theta function.Chapter 3,by using the arithmetic relations between overpartition function p(n)with the number of representations of n as sum of squares r3(n)and r5(n),this chapter investigate systematically some infinite families of congruences modulo 12,24 and 40 for p(n).Chapter 4,summarizes the work of this paper and gives several new ideas.