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arXiv · 2310.15545

Bushnell-Reiner zeta functions over two-dimensional semilocal rings

Sean B. Lynch
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Abstract

Lustig gave an infinite product formula for the zeta function of a commutative two-dimensional regular local ring with finite residue field. We extend this to the noncommutative setting with a method based on filtration by an invertible ideal. One application gives an abstract two-dimensional analogue of Hey's formula. Another application provides effective formulae for zeta functions over Rump's two-dimensional regular semiperfect rings. In the appendices, we supplement these two-dimensional applications with requisite one-dimensional calculations.

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Sean B. Lynch. 2023-10-24. Bushnell-Reiner zeta functions over two-dimensional semilocal rings. https://arxiv.org/abs/2310.15545

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