Differential modular forms on Shimura curves, I

被引：8
作者：
Buium, A [1 ]
机构：
[1] Univ New Mexico, Albuquerque, NM 87131 USA
来源：
COMPOSITIO MATHEMATICA | 2003年 / 139卷 / 02期
基金：
美国国家科学基金会;
关键词：
isogeny; modular forms; Shimura curves;
D O I：
10.1023/B:COMP.0000005081.66740.9a
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The quotient of a Shimura curve by the isogeny equivalence relation is not an object of algebraic geometry. The paper shows how this quotient space becomes a geometric object in a more general geometry obtained from 'usual algebraic geometry', by adjoining a new operation; this operation looks like a 'Fermat quotient' and should be viewed as an arithmetic analogue of usual derivations.
引用
收藏
页码：197 / 237
页数：41
相关论文
共 50 条
[41]   Shimura lifting on weak Maass forms [J].
Choie, Youngju ;
Lim, Subong .
ACTA ARITHMETICA, 2016, 173 (01) :1-18
[42]   DIFFERENTIAL OPERATORS ON MODULAR FORMS ASSOCIATED TO THETA SERIES [J].
Lee, Min Ho .
FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2015, 52 (01) :75-82
[43]   An Algorithm to Prove Holonomic Differential Equations for Modular Forms [J].
Paule, Peter ;
Radu, Cristian-Silviu .
TRANSCENDENCE IN ALGEBRA, COMBINATORICS, GEOMETRY AND NUMBER THEORY, TRANS19, 2021, 373 :367-420
[44]   Differential modular forms attached to newforms mod p [J].
Buium, Alexandru .
JOURNAL OF NUMBER THEORY, 2015, 155 :111-128
[45]   Ramanujan-type identities for Shimura curves [J].
Yang, Yifan .
ISRAEL JOURNAL OF MATHEMATICS, 2016, 214 (02) :699-731
[46]   A p-adic Maass-Shimura operator on Mumford curves [J].
Longo, Matteo .
ANNALES MATHEMATIQUES DU QUEBEC, 2023, 47 (01) :139-175
[47]   HEEGNER POINTS AND JOCHNOWITZ CONGRUENCES ON SHIMURA CURVES [J].
Vigni, Stefano .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2014, 142 (12) :4113-4126
[48]   COHERENT COHOMOLOGY OF SHIMURA VARIETIES AND AUTOMORPHIC FORMS [J].
Su, Jun .
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2024, 57 (04) :1039-1099
[49]   Differential formula for weakly modular forms of weight 16 and 20 [J].
Ahmed, Ambreen ;
Aygunes, Aykut Ahmet ;
Chaudhary, M. P. .
PERIODICA MATHEMATICA HUNGARICA, 2025,
[50]   Modular Forms and Weierstrass Mock Modular Forms [J].
Clemm, Amanda .
MATHEMATICS, 2016, 4 (01)
12345