Research Interest
My field of research at Temple University is Analytic Number Theory mainly Modular Functions. My advisor is Dr. Marvin Knopp.
Definitions
Analytic Number Theory: It involves the study of the Riemann zeta function and other similar functions such as Dirichlet series. The zeta function may be defined on half the complex plane as the sum 1 + 1/2s + 1/3s + 1/4s + ...; its connection with number theory results from its factorization as a product Prod(1 - 1/p^s )^(-1), the product taken over all primes p. Thus for example the distribution of the primes among the integers can be deduced from a good understanding of the behaviour of zeta(s). The Riemann Hypothesis states that zeta(s) is never zero except along the line Re(s)=1/2 (or at the negative even integers). This is arguably the most important open question in mathematics. There are other related functions, useful either for studying the Riemann zeta function or for making similar conclusions about other sets; for example, one may use them to prove the infinitude of primes in candidate linear progressions.
Modular functions: Modular Functions are closely
analogous to elliptic functions, where we choose a slightly different
domain of definition (H instead of C) and symmetry group 
.
Modular and elliptic functions are both special cases of the concept of an
automorphic function, which is a meromorphic function of 1 or more
complex variables defined on a particular complex manifold and invariant
under a particular group of analytic transformations (symmetries) of the
manifold.
Books and References
1) Introduction to Analytic Number Theory by Tom Apostol
2) Modular Functions and Dirichlet Series in Number Theory by Tom Apostol
3) Lectures in Dirichlet Series, Modular Functions And Quadratic Forms by Eriche Hecke
4) Modular Functions by Marvin Knopp
5) Elliptic Modular Functions: An Introduction (Grundlehren Der Mathematischen Wissenchaften Series, Vol 203) by B.Schoenberg, J.R. Smart, E. Schwandt
6) A First Course in Modular Forms Fred Diamond and Jerry Shurman
7) Introduction to the Arithmatic Theory of Automorphic Functions by Goro
Shimura