Slopes of modular forms and the ghost conjecture (unabridged version)

TL;DR

This paper proposes a unifying conjecture on the slopes of overconvergent p-adic cusp forms across all weights, connecting previous conjectures on classical slopes and boundary behaviors in weight space.

Contribution

It introduces a comprehensive conjecture that generalizes and unifies existing conjectures on slopes of p-adic cusp forms in the Gamma_0(N)-regular case.

Findings

Formulation of a new conjecture on slopes of overconvergent p-adic cusp forms

Unification of Buzzard's classical slope conjecture with boundary slope conjectures

Provides a framework for understanding slopes across all p-adic weights

Abstract

We formulate a conjecture on slopes of overconvergent p-adic cuspforms of any p-adic weight in the Gamma_0(N)-regular case. This conjecture unifies a conjecture of Buzzard on classical slopes and more recent conjectures on slopes "at the boundary of weight space".