Hecke fields of Hilbert modular analytic families

被引：6

作者：

Hida, Haruzo ^{[1
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

来源：

AUTOMORPHIC FORMS AND RELATED GEOMETRY: ASSESSING THE LEGACY OF I.I. PIATETSKI-SHAPIRO | 2014年 / 614卷

关键词：

ADIC L-FUNCTIONS;

D O I：

10.1090/conm/614/12251

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Take a non CM p-slope 0 analytic family of Hilbert modular forms of level np(infinity) for a prime p of the base totally real field F. We prove that the Hecke field over Q[u(p)infinity] of members of the family grows indefinitely large over any infinite set of arithmetic points with fixed weight. The condition: p > 2 made in [H11] for F = Q is also eliminated in this paper for the assertion.

引用

页码：97 / 137

页数：41

共 50 条

[31] Gevrey and analytic local models for families of vector fields
Bonckaert, P.
De Maesschalck, P.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2008, 10 (2-3): : 377 - 400
[32] On Hecke's modular functions, zeta functions, and some other analytic functions in the theory of numbers
Mordell, LJ
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1931, 32 : 501 - 556
[33] HECKE OPERATORS ON MODULAR FORMS
HSIAO, HJ
LEE, HC
ARCHIV DER MATHEMATIK, 1979, 32 (02) : 158 - 165
[34] Modular symbols and Hecke operators
Gunnells, PE
ALGORITHMIC NUMBER THEORY, 2000, 1838 : 347 - 357
[35] Shimura lift of real analytic Poincaré series and Hilbert modular Eisenstein series
Roland Matthes
Mathematische Zeitschrift, 1998, 229 : 547 - 574
[36] ON THE BLOCKS OF MODULAR HECKE ALGEBRAS
KHAMMASH, AA
JOURNAL OF ALGEBRA, 1993, 155 (02) : 545 - 554
[37] Shimura lift of real analytic Poincare series and Hilbert modular Eisenstein series
Matthes, R
MATHEMATISCHE ZEITSCHRIFT, 1998, 229 (03) : 547 - 574
[38] ON ARITHMETIC GENUS OF HILBERT MODULAR VARIETIES ON CYCLIC NUMBER-FIELDS
FENG, KQ
SCIENTIA SINICA SERIES A-MATHEMATICAL PHYSICAL ASTRONOMICAL & TECHNICAL SCIENCES, 1984, 27 (06): : 576 - 584
[39] Computing Hilbert modular forms over fields with nontrivial class group
Dembele, Lassina
Donnelly, Steve
ALGORITHMIC NUMBER THEORY, 2008, 5011 : 371 - +
[40] Families and blocks of Hecke algebras
Rouquier, R
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 329 (12): : 1037 - 1042

← 1 2 3 4 5 →