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On the Artin formalism for triple product $p$-adic $L$-functions: Chow--Heegner points vs. Heegner points (2409.08645v1)
Published 13 Sep 2024 in math.NT
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.