Transcendental Numbers and Special Analytic Functions

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DMS-0340812Papanikolas, Matthew A.Abstract:Title: Transcendental numbers and special analytic functionsThe investigator proposes to work on severalproblems about transcendental numbers and specialvalues of analytic functions, in order tounderstand the many links between analytic andarithmetic quantities. In one project, thisresearch explores properties of numbers arising inpositive characteristic from Anderson-Drinfeldmotives, such as periods and logarithms, and inparticular focuses on the algebraic relationsamong Carlitz logarithms. Furthermore, incollaboration with N. Ramachandran, theinvestigator plans to study the relationshipsbetween extension groups of abelian varieties overnumber fields and special values of HeckeL-functions and Rankin-Selberg L-functions.One of the fundamental branches of modernmathematics, number theory serves as the basis formany applications, including cryptography andcoding theory. The proposed research considersquestions involving the interplay betweenarithmetic and analytic aspects of number theory,which have their beginnings in classical work ofEuler and Gauss. Several parts of the projectlead naturally to problems for graduate andundergraduate research.