Comparison between the classical and characteristic p Riemann hypotheses, by David Goss

A revised version of this preprint appears as preprint 0196 and so this version has been removed. We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic $p$ $L$-series associated to function fields over a finite field. These analogs are based on the use of absolute values. Further we use absolute values to give similar formulations of the classical conjectures. We show how both sets of conjectures behave in remarkably similar ways.

David Goss <>