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

2016/07/15 by John Bergdall, Bergdall, John, Robert Pollack +1
Mathematics · #11F33 (primary) #11F85 (secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1607.04658

openalex publication_date 2016/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate a conjecture on slopes of overconvergent p-adic cuspforms of any p-adic weight in the Gamma₀(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".

Citations

• Where the Slopes Are
• Slopes of eigencurves over boundary disks

Related

• Slopes of modular forms and the Ghost conjecture
• Slopes of modular forms and reducible Galois representations: an oversight in the ghost conjecture
• Slopes of modular forms and geometry of eigencurves
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• Slopes of overconvergent 2-adic modular forms