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We provide the explicit formula for orbital integrals associated with elliptic regular semisimple elements in GLₙ(F) ∩ Mₙ(o) and associated with arbitrary elements of the spherical Hecke algebra of GLₙ(F) when $n=2, 3$, using results of [CKL]. Here F is a non-Archimedean local field of any characteristic with o its ring of integers.
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Cho et al. (2024) studied this question.
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