Zeta functions and L-series in positive characteristic

Explicit Formulae for the L-series in Positive Characteristic

speaker: Rudolph Perkins (Ohio State University)

abstract: We will study the \(L\)-series in \(1\leq  q\) indeterminates introduced by F. Pellarin. We will demonstrate how the Wagner series expansion for the character \(\chi_t\) appearing in F. Pellarin’s \(L\)-series gives rise to both generating series for the power sums occurring in these \(L\)-series series and also a method for determining the explicit rational functions arising as special values of these \(L\)-series. It is now known, due to results of B. Angles and F. Pellarin, that these \(L\)-series take rational values in great generality, and if time permits we shall discuss what’s needed to move our method to the case of \( s > q\) indeterminates.

timetable:
Wed 28 Nov, 10:45 - 12:00, Sala Conferenze Centro De Giorgi
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