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arXiv · 2409.08645

On the Artin formalism for triple product $p$-adic $L$-functions: Chow--Heegner points vs. Heegner points

Kâzım Büyükboduk·Daniele Casazza·Aprameyo Pal·Carlos de Vera-Piquero
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Abstract

Our main objective in this paper (which is expository for the most part) is to study the necessary steps to prove a factorization formula for a certain triple product $p$-adic $L$-function guided by the Artin formalism. The key ingredients are: a) the explicit reciprocity laws governing the relationship of diagonal cycles and generalized Heegner cycles to $p$-adic $L$-functions; b) a careful comparison of Chow--Heegner points and twisted Heegner points in Hida families, via formulae of Gross--Zagier type.

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Kâzım Büyükboduk, Daniele Casazza, Aprameyo Pal, Carlos de Vera-Piquero. 2024-09-13. On the Artin formalism for triple product $p$-adic $L$-functions: Chow--Heegner points vs. Heegner points. https://arxiv.org/abs/2409.08645

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