Transcendental Numbers and Special Analytic Functions

Texas A&M Research Foundation, College Station TX

Investigators

Abstract

DMS-0340812 Papanikolas, Matthew A. Abstract: Title: Transcendental numbers and special analytic functions The investigator proposes to work on several problems about transcendental numbers and special values of analytic functions, in order to understand the many links between analytic and arithmetic quantities. In one project, this research explores properties of numbers arising in positive characteristic from Anderson-Drinfeld motives, such as periods and logarithms, and in particular focuses on the algebraic relations among Carlitz logarithms. Furthermore, in collaboration with N. Ramachandran, the investigator plans to study the relationships between extension groups of abelian varieties over number fields and special values of Hecke L-functions and Rankin-Selberg L-functions. One of the fundamental branches of modern mathematics, number theory serves as the basis for many applications, including cryptography and coding theory. The proposed research considers questions involving the interplay between arithmetic and analytic aspects of number theory, which have their beginnings in classical work of Euler and Gauss. Several parts of the project lead naturally to problems for graduate and undergraduate research.