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INTERPOLATION OF NUMBERS OF CATALAN TYPE IN A LOCAL FIELD OF POSITIVE CHARACTERISTIC
 

Summary: INTERPOLATION OF NUMBERS OF CATALAN TYPE IN A
LOCAL FIELD OF POSITIVE CHARACTERISTIC
GREG W. ANDERSON
Abstract. Let k be a locally compact topological field of positive charac­
teristic. Let L be a cocompact discrete additive subgroup of k. Let U be
an open compact additive subgroup of k. Let #, u and a be elements of k,
with a nonzero. We study the behavior of the product
Q 0#=x#(#+L)#a(u+U) x
as a varies, using tools from local class field theory and harmonic analysis.
Typically ratios of such products occur as partial products grouped by degree
for the infinite products representing special values of Gamma­functions for
function fields. Our main result provides local confirmation for a two­variable
refinement of the Stark conjecture in the function field case recently proposed
by the author.
Contents
1. Introduction 1
2. Theta and Catalan symbols 6
3. Shadow theta and Catalan symbols 18
4. Interpolability and related notions 32
5. Concrete examples of strict interpolation 36

  

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

 

Collections: Mathematics