L-functions in Positive Characteristic

Meeting Details

For more information about this meeting, contact Rachel Weaver, Federico Rodriguez Hertz, Wen-Ching W. Li.

Speaker: Matt Papanikolas, Texas A&M University

Abstract: The study of L-functions and their special values has been a topic of significant interest to number theorists going back at least to Euler. During the 1970's and 1980's, Goss transported some of these ideas to the setting of function fields in positive characteristic and developed a theory of L-functions associated to Drinfeld modules, defined by Dirichlet series that take values in a function field instead of the complex numbers. Goss was inspired by the Carlitz zeta function, initially defined in the 1930's by Carlitz and itself an analogue of the Riemann zeta function. However, other than a few isolated results about the Carlitz zeta function and some related Goss L-functions, little was understood about the arithmetic nature of special values of Goss L-functions until breakthrough work of Taelman in 2012. Also in 2012, Pellarin defined a new class of L-functions taking values in Tate algebras by twisting the Carlitz zeta function by additional variables and proved several intriguing special value formulas. In this talk we will discuss the results of Goss, Pellarin, Taelman, and others, and present more recent advancements in special L-values of Goss and Pellarin L-functions.

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Room Reservation Information

Room Number: 114 McAllister

Date: 05/01/2025

Time: 3:30pm - 4:30pm