The number theory group at Oklahoma State University has established a thriving program of research, including a regular seminar series featuring lectures of both a research and expository nature by the resident number theorists, as well as frequent lectures by distinguished young and senior number theorists from around the country.
All six members of the group have received NSF support. Three have received Sloan fellowships. Members of this group have played key roles in securing two recent NSF computer equipment grants for our department. Number theory is famed not just for the beauty of its theorems, but for the enormous wealth and variety of techniques involved in discovering and proving these theorems. Number theory has drawn on and inspired developments in complex analysis, harmonic analysis, representation theory, and algebraic geometry. There is ample opportunity at Oklahoma State University to gain the broad understanding of modern mathematics necessary to pursue research in number theory.
Our faculty is prepared to offer courses in algebraic number theory, class field theory, analytic number theory, the arithmetic of elliptic curves as well as other arithmetic algebraic varieties, p-adic analysis, automorphic and modular forms, discrete subgroups of algebraic groups, computational number theory, as well as many other subfields of number theory.
Faculty:
Alan Adolphson: L-functions of algebraic varieties over finite
fields, using cohomological techniques; exponential sums, using both p-adic
and l-adic cohomologies. The variation of cohomology within a family of
varieties, involving, among other things,
the classical Fuchs-Picard differential equation.
James Cogdell: Automorphic representations and L-functions,
including L-functions for automorphic
representations of GL(n). Extension of Hecke's converse theorem to GL(n);
applications of this converse theorem to liftings of automorphic forms
and indirectly to class field theory. Rankin-Selberg theory of L-functions
for classical groups; application of theta liftings to arithmetic.
Brian Conrey: Classical problems of analytic number theory:
Mean-values and distribution of zeroes of the Riemann zeta function (or
more general zeta or L-functions). Automorphic forms.
Amit Ghosh: Analytic number theory: Relations between arithmetic
and harmonic analysis, for example analysis of L-functions (of number fields,
automorphic forms, etc.) to see the arithmetic they contain. Distribution
of zeros of the Riemann zeta function; automorphic L-functions.
Anthony Kable: Automorphic representations and L-functions,
including L-functions for automorphic
representations of GL(n). Quartic number fields.
David Wright: The relation between algebraic number theory and
algebraic groups. Distribution of cubic extensions of number fields, using
the theory of equivalence of binary cubic forms. Using
``zeta functions'' associated with representations of algebraic
groups to prove theorems about algebraic number fields.