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

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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 ℓ, u and a be elements of k, with a nonzero. We study the behavior of the product ∏₀≠ ₓ∈ ₍ℓ₊ₗ₎∩ 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).