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

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

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 relation...

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Hauptverfasser: Büyükboduk, Kâzım, Casazza, Daniele, Pal, Aprameyo, de Vera-Piquero, Carlos
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Pal, Aprameyo
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description 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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title On the Artin formalism for triple product $p$-adic $L$-functions: Chow--Heegner points vs. Heegner points
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