Date of Award
11-2015
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Mathematical Sciences
First Advisor
Dr. Mohamed El Bachraoui
Second Advisor
Dr. Kanat Abdukhalikov
Third Advisor
Dr. James Griffin
Abstract
In this report we shall introduce q-series and we shall discuss some of their applications to the integer partitions, the sums of squares, and the binomial coefficients. We will present the basic theory of q-series including the most famous theorems and rules governing these objects such as the q-binomial theorem and the Jacobi’s triple identity. We shall present the q-binomial coefficients which roughly speaking connect the binomial coefficients to q-series, we will give the most important results on q-binomial coefficients, and we shall provide some of our new results on the divisibility of binomial coefficients. Moreover, we shall give some well-known applications of q-series to sums of two squares and to integer partitions such as Ramanujan’s modulo 5 congruence.
Recommended Citation
Saif Al Suwaidi, Amna Abdul Baset Saif, "Q-Series with Applications to Binomial Coefficients, Integer Partitions and Sums of Squares" (2015). Theses. 180.
https://scholarworks.uaeu.ac.ae/all_theses/180