##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory

## Nathan Green

#### Texas A&M University

## Tensor Powers of Drinfeld Modules and Zeta Values

##### Abstract:

We study tensor powers of rank 1 Drinfeld A-modules, where A is the affine coordinate ring of an elliptic curve. Using the theory of A-motives, we find explicit formulas for the A-action of these modules. Then, by developing the theory of vector valued Anderson generating functions, we give formulas for the coefficients of the logarithm and exponential functions associated to these A-modules, as well as formulas for the fundamental period. This allows us to relate function field zeta values to evaluations of the logarithm function and prove transcendence facts about these zeta values.

Host: Cristian D. Popescu

### January 11, 2018

### 1:00 PM

### AP&M 7321

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