Computations on overconvergence rates related to the Eisenstein family
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Computations on overconvergence rates related to the Eisenstein family. / Advocaat, Bryan.
I: Journal of Number Theory, Bind 259, 2024, s. 112-130.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Computations on overconvergence rates related to the Eisenstein family
AU - Advocaat, Bryan
N1 - Publisher Copyright: © 2024 Elsevier Inc.
PY - 2024
Y1 - 2024
N2 - We provide for primes p≥5 a method to compute valuations appearing in the “formal” Katz expansion of the family [Formula presented] derived from the family of Eisenstein series Eκ⁎. 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.
AB - We provide for primes p≥5 a method to compute valuations appearing in the “formal” Katz expansion of the family [Formula presented] derived from the family of Eisenstein series Eκ⁎. 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.
KW - Computations
KW - Eisenstein series
KW - Overconvergent modular forms
U2 - 10.1016/j.jnt.2023.12.005
DO - 10.1016/j.jnt.2023.12.005
M3 - Journal article
AN - SCOPUS:85184866229
VL - 259
SP - 112
EP - 130
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
ER -
ID: 382976205