Mathematics – Number Theory
Scientific paper
1999-07-02
Journal of Number Theory, vol. 82 (June 2000), 299-322
Mathematics
Number Theory
This is the final version (with new title) as it will appear in the Journal of Number Theory
Scientific paper
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.
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