##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Rudy Perkins

#### Ohio State University

## On certain operators resembling polylogarithms in function field arithmetic.

##### Abstract:

Building on the work which will appear in my thesis and certain formalism introduced in F. Pellarin's paper \textit{Values of certain $L$-series in positive characteristic}, I will introduce a family arising from the Carlitz module in the ring of twisted power series over the ring $K$ of rational functions in one indeterminate with coefficients in a finite field. I will describe how this family gives rise to both the explicit calculation of the rational functions appearing (inexplicitly) in Pellarin's main result in the paper above and also to certain $K$-relations between Thakur's multizeta values originally introduced in his book \textit{Function Field Arithmetic}. This is a joint work with F. Pellarin.

Host: Cristian Popescu

### May 2, 2013

### 3:00 PM

### AP&M 7321

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