Article,
Computations on overconvergence rates related to the Eisenstein family
Affiliations
- [1] Univ Copenhagen, Dept Math Sci, Univ PK 5, DK-2100 Copenhagen O, Denmark [NORA names: KU University of Copenhagen; University; Denmark; Europe, EU; Nordic; OECD];
- [2] Univ Luxembourg, Dept Math, Maison Nombre,6 Ave Fonte, L-4364 Esch Sur Alzette, Luxembourg [NORA names: Luxembourg; Europe, EU; OECD]
Abstract
We provide for primes p >= 5 a method to compute valuations appearing in the "formal" Katz expansion of the family E kappa * derived from the family of Eisenstein series E kappa*. We will describe two algorithms: the first one to compute the Katz expansion of an overconvergent modular form and the second one, which uses the first algorithm, to compute valuations appearing in the "formal" Katz expansion. Based on data obtained using these algorithms we make a precise conjecture about a constant appearing in the overconvergence rates related to the classical Eisenstein series at level p. The study of these overconvergence rates of the members of this family goes back to a conjecture of Coleman.
Keywords
Computations,
Eisenstein series,
Overconvergent modular forms