Special Values of L-Series in Positive Characteristic

Start: 04/04/2018 - 4:15pm
End  : 04/04/2018 - 5:15pm


Matthew Papanikolas (Texas A&M University)


There are many parallels between the theories of the integers and the polynomial ring in one variable over a finite field.  In the 1930's Carlitz constructed function field valued analogues of the Riemann zeta function, and in 1980's Goss greatly generalized Carlitz's zeta function to L-functions associated to Drinfeld modules.  It is a natural question to ask how special values of Goss L-series capture arithmetic invariants of their underlying objects.  In spite of tantalizing examples, this remained a mystery for many years, until Taelman proved a class number formula for special values in 2012.  In this talk we will survey the history of Goss L-series and discuss the advances of Taelman, as well as further directions defined by Pellarin on deformations of Goss L-series.  We will also present results on log-algebraic identities for L-series attached to Drinfeld modules (joint with C.-Y. Chang and A. El-Guindy).

Freeberg Forum, LC 62, Kravis Center, CMC

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