Classical congruences for parameters in binary quadratic forms

被引：6

作者：

Evans, R ^{[1
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2001年 / 7卷 / 01期

关键词：

D O I：

10.1006/ffta.2000.0289

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Q(root -k) be an imaginary quadratic field with discriminant -k and class number h, with k not equal 3, 4, or 8. Let p be a prime such that (-k/p) = 1. There are integers C, D, unique up to sign, such that 4p(h) = C-2 + kD(2) P X C. Stickelberger gave a congruence for C module p which extends congruences of Gauss, Jacobi, and Eisenstein. Stickelberger also gave a simultaneous congruence for C module k, but only for prime k. We prove an extension of his result that holds for all k, giving along the way an exposition of his work. (C) 2000 Academic Press.

引用

页码：110 / 124

页数：15