##### Department of Mathematics,

University of California San Diego

****************************

### Math 209 - Number Theory

## Keith Conrad

#### UCSD

## Revisiting the Gross-Koblitz formula

##### Abstract:

The Gross-Koblitz formula describes Gauss sums on finite fieldsof characteristic $p$ in terms of the $p$-adic Gamma function. Thisformula is a $p$-adic lifting of Stickelberger's congruence on Gauss sums.There have been several proofs of the formula (Gross-Koblitz,Dwork-Boyarsky, Katz, Coleman), which all involve some cohomologicalcalculations. Recently, a proof has been found by A. Robert which isconceptual but truly elementary, at the level of "freshman $p$-adicanalysis." We will discuss Robert's proof and describe possibleextensions

Host:

### February 6, 2003

### 2:00 PM

### AP&M 7321

****************************