The exceptional zero conjecture for Hilbert modular forms

被引：21
作者：
Mok, Chung Pang [1 ]
机构：
[1] Univ Calif Berkeley, Berkeley, CA 94720 USA
来源：
COMPOSITIO MATHEMATICA | 2009年 / 145卷 / 01期
关键词：
ADIC L-FUNCTIONS; TOTALLY-REAL FIELDS; CURVES; TOWERS; VALUES;
D O I：
10.1112/S0010437X08003813
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Using a p-adic analogue of the convolution method of Rankin-Selberg and Shimura, we construct the two-variable p-adic L-function of a Hida family of Hilbert modular eigenforms of parallel weight. It is shown that the conditions of Greenberg-Stevens [R. Greenberg and G. Stevens, p-adic L-Junctions and p-adic periods of modular forms, Invent. Math. 111 (1993), 407-447] are satisfied, from which we deduce special cases of the Mazur-Tate-Teitelbaum conjecture in the Hilbert modular setting.
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页码：1 / 55
页数：55
相关论文
共 23 条
[1]   MOTIVES FOR HILBERT MODULAR-FORMS [J].
BLASIUS, D ;
ROGAWSKI, JD .
INVENTIONES MATHEMATICAE, 1993, 114 (01) :55-87
[2]  
Blasius D., 2006, ASPECTS MATH E, V37, P35
[3]  
CARAYOL H, 1986, ANN SCI ECOLE NORM S, V19, P409
[4]  
CARAYOL H, 1986, COMPOS MATH, V59, P151
[5]   S-adic L-functions attached to the symmetric square of a newform [J].
Dabrowski, A ;
Delbourgo, D .
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1997, 74 :559-611
[6]   P-ADIC L-FUNCTIONS OF HILBERT MODULAR-FORMS [J].
DABROWSKI, A .
ANNALES DE L INSTITUT FOURIER, 1994, 44 (04) :1025-1041
[7]   VALUES OF ABELIAN L-FUNCTIONS AT NEGATIVE INTEGERS OVER TOTALLY-REAL FIELDS [J].
DELIGNE, P ;
RIBET, KA .
INVENTIONES MATHEMATICAE, 1980, 59 (03) :227-286
[8]   P-ADIC L-FUNCTIONS AND P-ADIC PERIODS OF MODULAR-FORMS [J].
GREENBERG, R ;
STEVENS, G .
INVENTIONES MATHEMATICAE, 1993, 111 (02) :407-447
[9]  
Greenberg R., 1994, CONTEMP MATH-SINGAP, V165, P183, DOI [10.1090/conm/165/01607, DOI 10.1090/CONM/165/01607]
[10]   FACTORIZATION OF P-ADIC L-SERIES [J].
GROSS, BH .
INVENTIONES MATHEMATICAE, 1980, 57 (01) :83-95
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