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arXiv · 2604.15079

On local integrability results for $p$-adic reductive groups

Cheng-Chiang Tsai
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Abstract

We present a short proof, based on local character expansions, of the celebrated theorem of Harish-Chandra about local integrability of complex characters of $p$-adic reductive groups. The proof gives an algebraic incarnation of the local integrability that works for some coefficients different from $\mathbb{C}$, verifies local integrability in cases that appear not covered in the literature, and shows that a character is locally-$L^{\alpha}$ for some specified $\alpha>1$ as in [GGH23].

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BibTeXRIS

Cheng-Chiang Tsai. 2026-04-16. On local integrability results for $p$-adic reductive groups. https://arxiv.org/abs/2604.15079

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