A rational reciprocity law over function fields

被引：0
作者：
Yoshinori Hamahata
机构：
[1] Okayama University of Science,Department of Applied Mathematics
来源：
Archiv der Mathematik | 2017年 / 108卷
关键词：
Power residues; Rational reciprocity law; Function fields; Primary 11A15; Secondary 11R58;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In the classical case, reciprocity laws for power residue symbols are called rational, which means that the power residue symbols only assume the values ±1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\pm 1}$$\end{document} and have entries in Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Z}}$$\end{document}. We establish a rational reciprocity law over function fields.
引用
收藏
页码：233 / 240
页数：7
相关论文
共 13 条
[1]  
Artin E.(1924)Quadratische Körper im Gebiete der höheren Kongruenzen Math. Z. 19 153-246
[2]  
Brown E.(1972)Quadratic forms and biquadratic reciprocity J. Reine Angew. Math. 253 214-220
[3]  
Burde K.(1969)Ein rationales biquadratisches Reziprozitätsgesetz J. Reine Angew. Math. 235 175-184
[4]  
Dedekind R.(1857)Abriß einer Theorie der höheren Congruenzen in Bezug auf einen reellen Primzahl-Modulus J. Reine Angew. Math. 54 1-26
[5]  
Helou C.(1990)On rational reciprocity Proc. Amer. Math. Soc. 108 861-866
[6]  
Hsu C.-H.(2003)On polynomial reciprocity law J. Number Theory 101 13-31
[7]  
Lehmer E.(1971)On the quadratic character of some quadratic surds J. Reine Angew. Math. 250 42-48
[8]  
Lehmer E.(1978)Rational reciprocity laws Amer. Math. Monthly 85 467-472
[9]  
Lemmermeyer F.(1994)Rational quartic reciprocity Acta Arithmetica 67 387-390
[10]  
Williams K.(1976)A rational octic reciprocity law Pacific J. Math. 63 563-570
12