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arXiv · 2501.06541

On the Artin formalism for triple product $p$-adic $L$-functions

Kâzım Büyükboduk·Ryotaro Sakamoto
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Abstract

Our main objective in the present article is to study the factorisation problem for triple-product $p$-adic $L$-functions, particularly in the scenarios when the defining properties of the $p$-adic $L$-functions involved have no bearing on this problem, although Artin formalism would suggest such a factorisation. Our analysis, which is guided by the ETNC philosophy, recasts this problem as a comparison of diagonal cycles, Beilinson--Kato elements, and Heegner cycles.

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Kâzım Büyükboduk, Ryotaro Sakamoto. 2026-07-27. On the Artin formalism for triple product $p$-adic $L$-functions. https://arxiv.org/abs/2501.06541

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