Triple product p-adic L-function attached to p-adic families of modular forms

TL;DR

This paper extends the construction of three-variable triple product p-adic L-functions to more general p-adic families of modular forms, broadening the scope of Hida's original work.

Contribution

It generalizes Hsieh's interpolation formulas to include a primitive Hida family and two additional p-adic families, enhancing the understanding of p-adic L-functions.

Findings

Constructed a new three-variable triple product p-adic L-function for broader families.

Proved interpolation formulas in the unbalanced case.

Extended the applicability of p-adic L-functions to more general modular forms.

Abstract

Ming-Lun Hsieh constructed three-variable triple product p-adic L-functions attached to triples of primitive Hida families and proved interpolation formulas. We generalize his result in the unbalanced case and construct a three-variable triple product p-adic L-function attached to a primitive Hida family and two more general p-adic families of modular forms.