Zhiwei Yun
Published 2013-03-11, updated 2013-03-12Version 2
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.
A modular relation involving non-trivial zeros of the Dedekind zeta function, and the Generalized Riemann Hypothesis
On 2-dimensional 2-adic Galois representations of local and global fields
Riemann-Roch and Riemann-Hurwitz theorems for global fields
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