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

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

Number Theory 2024-09-16 v1

Authors: Kâzım Büyükboduk , Daniele Casazza , Aprameyo Pal , Carlos de Vera-Piquero

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.

Keywords

Artin formalism triple product p-adic L-function Chow-Heegner points Heegner points Gross-Zagier formula

Cite

@article{arxiv.2409.08645,
  title  = {On the Artin formalism for triple product $p$-adic $L$-functions: Chow--Heegner points vs. Heegner points},
  author = {Kâzım Büyükboduk and Daniele Casazza and Aprameyo Pal and Carlos de Vera-Piquero},
  journal= {arXiv preprint arXiv:2409.08645},
  year   = {2024}
}

Comments

To appear in the Proceedings of the conference "Arithmetic of L-functions", EMS Series of Congress Reports

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

Abstract

Keywords

Cite

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