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INTERPOLATION OF HYPERGEOMETRIC RATIOS IN A GLOBAL FIELD OF POSITIVE CHARACTERISTIC
 

Summary: INTERPOLATION OF HYPERGEOMETRIC RATIOS IN A
GLOBAL FIELD OF POSITIVE CHARACTERISTIC
GREG W. ANDERSON
Abstract. In connection with each global field of positive characteristic we
exhibit many examples of two-variable algebraic functions possessing proper-
ties consistent with a conjectural refinement of the Stark conjecture in the
function field case recently proposed by the author (math.NT/0407535). Most
notably, all examples are Coleman units. We obtain our results by studying
rank one shtukas in which both zero and pole are generic, i. e., shtukas not
associated to any Drinfeld module.
Contents
1. Introduction 1
2. Formulation of the main result 2
3. Discussion 8
4. Toolkit 12
5. Invariants of rank one shtukas 16
6. Proof of the main result 22
References 24
1. Introduction
Our main result (Theorem 2.5 below) provides in connection with each global

  

Source: Anderson, Greg W. - School of Mathematics, University of Minnesota

 

Collections: Mathematics