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arXiv · 2609.39539

Finite-slope p-adic L-functions for $\mathrm{GL}_{3}$

Xenia Dimitrakopoulou·Rob Rockwood
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Abstract

Let $Π$ be a regular algebraic cuspidal automorphic representation of $\mathrm{GL}_{3}(\mathbb{A}_{\mathbb{Q}})$ of weight $(a, 0, -a)$, and let $p$ be a prime. Generalising work of Loeffler--Williams in the nearly-ordinary case, we construct $p$-adic $L$-functions for each small slope regular $P_{1}$-refinement of $Π$ at $p$ consistent with the conjectures of Coates--Perrin-Riou and Panchishkin.

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Xenia Dimitrakopoulou, Rob Rockwood. 2026-09-30. Finite-slope p-adic L-functions for $\mathrm{GL}_{3}$. https://arxiv.org/abs/2609.39539

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