Research Interests: I study modular forms and their applications to problems relating to algebraic number theory, elliptic curves, L-functions, partitions, and other topics in number theory.

Department of Computer Science and Engineering

Research Interests: My interests in number theory are primarily in binary quadratic forms and the class groups of quadratic, cubic, and quartic number fields and in the application of number theory to cryptography and information security. I am also interested in the application of novel computer hardware to computational problems in number theory.

Research Interests: Number Theory, including Analytic, Classical Algebraic, Combinatorial, Computational, Elementary, and Transcedence topics. I have particular interests in results associated with lattice points close to (or on) a curve or surface, the distribution of special sequences of integers in short intervals, applications of Padé approximations to Number Theory, the irreducibility of polynomials over the rationals, and computations with sparse or lacunary polynomials.

Research Interests: Various aspects of Analytic and Algebraic Number Theory with particular focus on modern techniques in the distribution of primes and on applications of these techniques beyond their traditional settings.

Research Interests: Analytic Number Theory and Approximation Theory with particular interests in the use of finite differences to determine information about lattice points close to a curve or surface. I also have interests in the application of these results to gap problems in Number Theory.

In addition, there are a variety of other faculty members who have done some research in the area of Number Theory. These include Joshua Cooper, Jerry Griggs, Làszlò Szèkely, and Vladimir Temlyakov.

Graduate Course Descriptions in Number Theory

The following courses have run, at least one each semester, during the last several years. The particular material covered in one of these courses may vary with the professor. Click on a course to see a course description corresponding to a past course offering. A square to the left of the course listed indicates that class notes can also be obtained through the link.

For Ph.D. students, reading course options are also available. Reading courses have included investigations in Additive Number Theory, Diophantine Approximation, Exponential Sum Techniques, p-adic Analysis, Pretentiousness in Number Theory, and Sieve Methods.

We have regular Number Theory Seminars that include students, faculty, and visitors. In addition, there are regular regional Number Theory conferences in this area including PANTS , SERMON and INTEGERS . Many outstanding speakers from throughout North America present talks at these seminars and meetings. In addition, these outlets provide students and faculty alike with ample opportunities to give talks on their own research.

Some material related to past comprehensive exams in Number Theory at USC is also available to students.

Other graduate courses in our department are listed at this location.

Each year we also offer an undergraduate Math 580: Number Theory course.

More About Our Department And University

Some Other Links Of Interest

Last modified on 08/04/11.
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