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The Riemann Hypothesis for Function Fields by Machiel van Frankenhuijsen

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Introduction

The Riemann zeta function is the function ζ(s), defined for Re s > 1 by

image

It has a meromorphic continuation to the complex plane, with a simple pole at s = 1 with residue 1. Completing this function with the factor for the archimedean valuation, image one obtains the function

image (1)

The function image is meromorphic on with simple poles at 0 ...

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