On the elliptic Stark conjecture in higher weight

TL;DR

This paper investigates special values of a triple product p-adic L-function, proposing conjectural formulas extending the Elliptic Stark Conjecture and providing evidence through specific case proofs.

Contribution

It introduces conjectural formulas for these special values, extending the Elliptic Stark Conjecture, with partial theoretical validation.

Findings

Proposed new conjectural formulas for p-adic L-values

Proved particular cases supporting the conjectures

Extended the scope of the Elliptic Stark Conjecture

Abstract

We study the special values of the triple product $p$-adic $L$-function constructed by Darmon and Rotger at all classical points outside the region of interpolation. We propose conjectural formulas for these values that can be seen as extending the Elliptic Stark Conjecture, and we provide theoretical evidence for them by proving some particular cases.