Slopes of modular forms and the ghost conjecture

TL;DR

This paper proposes a unifying conjecture on the slopes of overconvergent p-adic cusp forms across all weights, linking previous conjectures by Buzzard and others about classical and boundary slopes.

Contribution

It introduces a new conjecture that 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".