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arXiv · 2310.17850

The Barnes-Hurwitz zeta cocycle at $s=0$ and Ehrhart quasi-polynomials of triangles

Milton Espinoza
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Abstract

Following a theorem of David R. Hayes, we give a geometric interpretation of the special value at $s=0$ of certain $1$-cocycle on $\mathrm{PGL}_2(\mathbb{Q})$ previously introduced by the author. This work yields three main results: an explicit formula for our cocycle at $s=0$, a generalization and a new proof of Hayes' theorem, and an elegant summation formula for the $0$th coefficient of the Ehrhart quasi-polynomial of certain triangles in $\mathbb{R}^2$.

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Milton Espinoza. 2023-10-27. The Barnes-Hurwitz zeta cocycle at $s=0$ and Ehrhart quasi-polynomials of triangles. https://arxiv.org/abs/2310.17850

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