A DETERMINANT FORMULA FOR RELATIVE CONGRUENCE ZETA FUNCTIONS FOR CYCLOTOMIC FUNCTION FIELDS

被引：1
|
作者：
Shiomi, Daisuke [1 ]
机构：
[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan
来源：
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2010年 / 89卷 / 01期
关键词：
congruence zeta function; cyclotomic function fields; CLASS NUMBER;
D O I：
10.1017/S1446788710000261
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Rosen gave a determinant formula for relative class numbers for cyclotomic function fields, which may be regarded as an analogue of the classical Maillet determinant. In this paper, we give a determinant formula for relative congruence zeta functions for cyclotomic function fields. Our formula may be regarded as a generalization of the determinant formula for the relative class number.
引用
收藏
页码：133 / 144
页数：12
相关论文
共 50 条
  • [21] On the Northcott property of zeta functions over function fields
    Genereux, Xavier
    Lalin, Matilde
    Li, Wanlin
    FINITE FIELDS AND THEIR APPLICATIONS, 2022, 83
  • [22] VANDIVERS CONGRUENCE FOR RELATIVE CLASS NUMBER OF PTH CYCLOTOMIC FIELD
    HASSE, H
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1966, 15 (01) : 87 - &
  • [23] Ordinary cyclotomic function fields
    Shiomi, Daisuke
    JOURNAL OF NUMBER THEORY, 2013, 133 (02) : 523 - 533
  • [24] Concerning the congruence zeta function.
    Hasse, H
    SITZUNGSBERICHTE DER PREUSSICHEN AKADEMIE DER WISSENSCHAFTEN PHYSIKALISCH-MATHEMATISCHE KLASSE, 1934, : 250 - 263
  • [25] On the subfields of cyclotomic function fields
    Zhao, Zhengjun
    Wu, Xia
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2013, 63 (03) : 799 - 803
  • [26] CYCLOTOMIC UNITS IN FUNCTION FIELDS
    Bae, Sunghan
    Yin, Linsheng
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (02) : 401 - 408
  • [27] On the subfields of cyclotomic function fields
    Zhengjun Zhao
    Xia Wu
    Czechoslovak Mathematical Journal, 2013, 63 : 799 - 803
  • [28] Group determinant formulas and class numbers of cyclotomic fields
    Jung, Hwan Yup
    Ahn, Jaehyun
    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2007, 44 (03) : 499 - 509
  • [29] Selberg zeta functions of PGL and PSL over function fields
    Koyama, SY
    NUMBER THEORY AND ITS APPLICATIONS, 1999, 2 : 253 - 261
  • [30] Multiple zeta functions and polylogarithms over global function fields
    Basak, Debmalya
    Degre-Pelletier, Nicolas
    Lalin, Matilde N.
    JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2020, 32 (02): : 403 - 438
12345