Slopes of modular forms and the ghost conjecture

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".

17 pages. 2 figures. Minor changes from v1. Final version. To appear in IMRN. arXiv admin note: text overlap with arXiv:1607.04658

References in corpus (5)

• Extended eigenvarieties for overconvergent cohomology
• The eigencurve over the boundary of weight space
• Arithmetic properties of Fredholm series for p-adic modular forms
• Computing overconvergent forms for small primes
• A remark on non-integral p-adic slopes for modular forms

Cited by in corpus (8)

• Slopes of modular forms and the ghost conjecture, II
• Upper bounds for constant slope $p$-adic families of modular forms
• A remark on non-integral p-adic slopes for modular forms
• Zeta functions of Z_p-towers of curves
• Slopes of overconvergent Hilbert modular forms
• Generic Newton Slopes for Artin-Schreier-Witt Tower in two variables
• An explicit computation of the Hecke operator and the ghost conjecture
• Newton Polygons of Hecke Operators