On extra zeros of p-adic L-functions: the crystalline case

TL;DR

This paper proposes a conjecture about additional zeros of p-adic L-functions at near central points, extending previous work, and demonstrates its consistency with Perrin-Riou's theoretical framework.

Contribution

It introduces a new conjecture on extra zeros of p-adic L-functions and shows its compatibility with existing p-adic L-function theory.

Findings

Conjecture generalizes previous hypotheses about zeros.

Compatibility established with Perrin-Riou's theory.

Provides a theoretical foundation for further research.

Abstract

We formulate a conjecture about extra zeros of p-adic L-functions at near central points which generalises the conjecture formulated in our previous paper. We prove that this conjecture is compatible with Perrin-Riou's theory of p-adic L-functions.