Computations with classical and p-adic modular forms

被引：18
|
作者：
Lauder, Alan G. B. [1 ]
机构：
[1] Math Inst, Oxford OX1 3LB, England
来源：
LMS JOURNAL OF COMPUTATION AND MATHEMATICS | 2011年 / 14卷
基金：
欧洲研究理事会;
关键词：
FAMILIES;
D O I：
10.1112/S1461157011000155
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We present p-adic algorithms for computing Hecke polynomials and Hecke eigenforms associated to spaces of classical modular forms, using the theory of overconvergent modular forms. The algorithms have a running time which grows linearly with the logarithm of the weight and are well suited to investigating the dimension variation of certain p-adically defined spaces of classical modular forms.
引用
收藏
页码：214 / 231
页数：18
相关论文
共 50 条
  • [41] Slopes of Modular Forms and the Ghost Conjecture
    Bergdall, John
    Pollack, Robert
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2019, 2019 (04) : 1125 - 1144
  • [42] OVERCONVERGENT MODULAR SHEAVES AND MODULAR FORMS FOR GL2/F
    Andreatta, Fabrizio
    Iovita, Adrian
    Stevens, Glenn
    ISRAEL JOURNAL OF MATHEMATICS, 2014, 201 (01) : 299 - 359
  • [43] Local ε-isomorphisms for rank two p-adic representations of Gal ((Q)over-barp/Qp) and a functional equation of Kato's Euler system
    Nakamura, Kentaro
    CAMBRIDGE JOURNAL OF MATHEMATICS, 2017, 5 (03) : 281 - 368
  • [44] $p$-ADIC $L$-FUNCTIONS FOR UNITARY GROUPS
    Eischen, Ellen
    Harris, Michael
    Li, Jianshu
    Skinner, Christopher
    FORUM OF MATHEMATICS PI, 2020, 8
  • [45] Fourier coefficients and slopes of Drinfeld modular forms
    Bandini, Andrea
    Valentino, Maria
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2023, : 2523 - 2553
  • [46] On certain finiteness questions in the arithmetic of modular forms
    Kiming, I.
    Rustom, N.
    Wiese, G.
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2016, 94 : 479 - 502
  • [47] HYPERELLIPTIC SCHOTTKY PROBLEM AND STABLE MODULAR FORMS
    Codogni, Giulio
    DOCUMENTA MATHEMATICA, 2016, 21 : 445 - 466
  • [48] Normal Forms, K3 Surface Moduli, and Modular Parametrizations
    Clingher, Adrian
    Doran, Charles F.
    Lewis, Jacob
    Whitcher, Ursula
    GROUPS AND SYMMETRIES: FROM NEOLITHIC SCOTS TO JOHN MCKAY, 2009, 47 : 81 - +
  • [49] ON SYMMETRIC POWER &ITL&IT-INVARIANTS OF IWAHORI LEVEL HILBERT MODULAR FORMS
    Harron, Robert
    Jorza, Andrei
    AMERICAN JOURNAL OF MATHEMATICS, 2017, 139 (06) : 1605 - 1647
  • [50] Iwasawa theory for symmetric powers of CM modular forms at nonordinary primes, II
    Harron, Robert
    Pottharst, Jonathan
    JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2016, 28 (03): : 655 - 677
12345