Interpolation of numbers of Catalan type in a local field of positive characteristic

Details Interpolation of numbers of Catalan type in a local field of positive characteristic Interpolation of numbers of Catalan type in a local field of positive characteristic

2006-01-19

arxiv.org/abs/math/0601479v2

Mathematics

Number Theory

LaTeX, 50 pages. v2: Introduction and last section rewritten, otherwise only some typos corrected. This is the final version,

Scientific paper

Let $k$ be a local field of positive characteristic. Let $L$ be a cocompact discrete subgroup of $k$. Let $U$ be an open compact subgroup of $k$. Let $\ell$, $u$ and $a$ be elements of $k$, with $a$ nonzero. We study the behavior of the product $\prod_{0\neq x\in (\ell+L)\cap a(u+U)}x$ as $a$ varies. Our main result, which blends harmonic analysis and local class field theory, provides local confirmation of a conjecture concerning global function fields recently made by the author (math.NT/0407535).

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