嵌入定理与代数数域上的大筛法

丁夏畦

数学学报 ›› 1979, Vol. 22 ›› Issue (4) : 448-458.

数学学报 ›› 1979, Vol. 22 ›› Issue (4) : 448-458. DOI: 10.12386/A1979sxxb0041
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嵌入定理与代数数域上的大筛法

    丁夏畦
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IMBEDDING THEOREMS AND THE LARGE SIEVE METHOD IN ALGEBRAIC NUMBER FIELDS

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<正> 本文把数理方程研究中常用的嵌入定理稍作推广,应用到代数数域上来,并把[4]中第四章的定理4.2和[1,5]中的均值定理推广到代数数域上. 为此,先介绍一些符号与约定,基本上采自[2]. 设K为-n次代数数域,按通常的记号,记作n=r_1+2r_2.以Z_k表K中的整数环. 1.设为一理想,如α,β∈Z_k,|(α-β),则记α≡β(mod ).按此可把K中的整数分类,其类数为N.Z_k中与互素的整数在上述分类中占住类数为

Abstract

In this paper we give a slight generalization of the imbedding theorem proved in [3]. And then we apply it to algebraic number fields, we obtaining a large sieve inequality. Finally we generalize to algebraic number fields the mean value theorem in [1] where with it we proved the Chen's theorem on Goldbaeh problem.

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丁夏畦. 嵌入定理与代数数域上的大筛法. 数学学报, 1979, 22(4): 448-458 https://doi.org/10.12386/A1979sxxb0041
IMBEDDING THEOREMS AND THE LARGE SIEVE METHOD IN ALGEBRAIC NUMBER FIELDS. Acta Mathematica Sinica, Chinese Series, 1979, 22(4): 448-458 https://doi.org/10.12386/A1979sxxb0041

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