##### Department of Mathematics,

University of California San Diego

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### RTG Colloquium

## Nathan Green

#### UCSD

## Special Values of L-functions over Drinfeld Modules

##### Abstract:

We work out an explicit theory for the shtuka function of rank 1 sign-normalized Drinfeld modules over the function field of an elliptic curve. Using these explicit formulas, we obtain a product formula for the fundamental period of the exponential function associated to the Drinfeld module. We also find identities for deformations of reciprocal sums and as a result prove special value formulas for L-series over the function field.

### October 23, 2019

### 2:00 PM

### AP&M 7321

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