  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 reformulations
of the classical conjectures (with, perhaps, finitely many exceptional zeroes).
We show how both sets of conjectures behave in remarkably similar ways.
