On the Artin formalism for triple product $p$-adic $L$-functions
Number Theory
2025-01-14 v1
Abstract
Our main objective in the present article is to study the factorization problem for triple-product -adic -functions, particularly in the scenarios when the defining properties of the -adic -functions involved have no bearing on this problem, although Artin formalism would suggest such a factorization. Our analysis, which is guided by the ETNC philosophy, recasts this problem as a comparison of diagonal cycles, Beilinson--Kato elements, and Heegner cycles.
Keywords
Cite
@article{arxiv.2501.06541,
title = {On the Artin formalism for triple product $p$-adic $L$-functions},
author = {Kâzım Büyükboduk and Ryotaro Sakamoto},
journal= {arXiv preprint arXiv:2501.06541},
year = {2025}
}
Comments
This is the first paper in a two-part series replacing an earlier submission (arXiv:2301.08383), which is no longer intended to be published as a stand-alone paper. 45 pages, comments are very welcome