 
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
