On the Artin formalism for triple product $p$-adic $L$-functions: Super-factorization

TL;DR

This paper proves a specific factorization conjecture for triple-product $p$-adic $L$-functions in cases involving complex multiplication, advancing understanding of their structure and relationships.

Contribution

It establishes the Artin formalism for triple product $p$-adic $L$-functions when two factors have complex multiplication, confirming a key conjecture.

Findings

Confirmed the factorization conjecture in the CM case

Demonstrated super-factorization property of $p$-adic $L$-functions

Enhanced understanding of the structure of triple product $p$-adic $L$-functions

Abstract

We prove the factorization conjecture for triple-product $p$-adic $L$-functions formulated in a companion article in the special case when two of the (three) factors have complex multiplication.