Orbital integrals and Dedekind zeta functions

Zhiwei Yun

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arXiv · 1303.2420

Orbital integrals and Dedekind zeta functions

Zhiwei Yun

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Abstract

Let F be a local non-archimedean field. We prove a formula relating orbital integrals in GL(n,F) (for the unit Hecke function) and the generating series counting ideals of a certain ring. Using this formula, we give an explicit estimate for such orbital integrals. We also derive an analogous formula for global fields, proving analytic properties of the Dedekind zeta function for orders in global fields.

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Zhiwei Yun. 2013-03-11. Orbital integrals and Dedekind zeta functions. https://arxiv.org/abs/1303.2420

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