Zeta functions and L-series in positive characteristic
timetable:
Tue 27 Nov, 10:45 - 12:00, Sala Conferenze Centro De Giorgi
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Interpolations of Carlitz-zeta values
speaker: Federico Pellarin (Université Jean Monnet, Saint-Etienne)abstract: In this talk, we will be focused on the various analytic ways we have to interpolate the sums \[\sum_{a\in A^+}a^{-\alpha}\in\mathbb{F}[[1/T]],\ \ \ \ a\in\mathbb{Z}_{>0},\] where \(A^+\) denotes the set of monic polynomials of \(\mathbb{F}_q[T]\) and how the analytic functions so introduced are expected to encode arithmetic properties of these sums. In particular, we will introduce a class of entire rigid analytic functions of several variables sharing similarities with the Hurwitz zeta function, and we will discuss about connections these functions have with 1) Drinfeld modular forms 2) the Carlitz module 3) Anderson-Thakur function 4) etc.
timetable:
Tue 27 Nov, 10:45 - 12:00, Sala Conferenze Centro De Giorgi
<< Go back