Chowla's theorem over function fields

被引：1

作者：

Hamahata, Yoshinori ^{[1
]}

机构：

[1] Okayama Univ Sci, Dept Appl Math, Ridai Cho 1-1, Okayama 7000005, Japan

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2018年 / 14卷 / 06期

关键词：

Chowla's theorem; L-function; function fields;

D O I：

10.1142/S1793042118501026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Sarvadaman Chowla proved that if p is an odd prime, then cot(2 pi j/p) (j = 1, . . . , (p - 1)/2) are linearly independent over the field of rational numbers. We establish an analog of this result over function fields. As an application, we prove an analog of the Baker-Birch-Wirsing theorem about the non-vanishing of Dirichlet series with periodic coefficients at s = 1 in the function field setup with a parity condition.

引用

页码：1689 / 1698

页数：10

共 50 条

[41] Finite descent obstruction for curves over function fields [J].

José Felipe Voloch .

Bulletin of the Brazilian Mathematical Society, New Series, 2012, 43 (1) :1-6

[42] Remarks on Fermat quotient operators over function fields [J].

Jeong, Sangtae ;

Li, Chunlan .

FINITE FIELDS AND THEIR APPLICATIONS, 2013, 23 :60-68

[43] Finite descent obstruction for curves over function fields [J].

Voloch, Jose Felipe .

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2012, 43 (01) :1-6

[44] Globalization of supercuspidal representations over function fields and applications [J].

Gan, Wee Teck ;

Lomeli, Luis .

JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2018, 20 (11) :2813-2858

[45] On the Bombieri-Pila method over function fields [J].

Sedunova, Alisa .

ACTA ARITHMETICA, 2017, 181 (04) :321-331

[46] Universality of L-functions over function fields [J].

Andrade, Julio C. ;

Gonek, Steven M. ;

Lee, Yoonbok .

ADVANCES IN MATHEMATICS, 2025, 471

[47] Ramanujan graphs and exponential sums over function fields [J].

Sardari, Naser T. ;

Zargar, Masoud .

JOURNAL OF NUMBER THEORY, 2020, 217 :44-77

[48] GALOIS GROUPS OVER FUNCTION FIELDS OF POSITIVE CHARACTERISTIC [J].

Conway, John ;

McKay, John ;

Trojan, Allan .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (04) :1205-1212

[49] CONTROL THEOREMS FOR ELLIPTIC CURVES OVER FUNCTION FIELDS [J].

Bandini, A. ;

Longhi, I. .

INTERNATIONAL JOURNAL OF NUMBER THEORY, 2009, 5 (02) :229-256

[50] ON THUE EQUATIONS OF SPLITTING TYPE OVER FUNCTION FIELDS [J].

Ziegler, Volker .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2010, 40 (02) :723-747

← 1 2 3 4 5 →