Uniform bounds in Waring's problem over some diagonal forms

被引：0

作者：

Pliego, Javier ^{[1
,2
]}

机构：

[1] Univ Bristol, Sch Math, Fry Bldg,Woodland Rd, Bristol BS8 1UG, Avon, England

[2] Purdue Univ, Dept Math, 150 N Univ St, W Lafayette, IN 47907 USA

来源：

MATHEMATISCHE ZEITSCHRIFT | 2022年 / 300卷 / 03期

基金：

欧洲研究理事会;

关键词：

Waring's problem; Hardy-Littlewood method; Diagonal forms; GOLDBACH PROBLEM; ITERATIVE METHOD; IMPROVEMENT; THEOREM; 7TH;

D O I：

10.1007/s00209-021-02887-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the existence of representations of every large positive integer as a sum of k-th powers of integers represented as certain diagonal forms. In particular, we consider a family of diagonal forms and discuss the problem of giving a uniform upper bound over the family for the number of variables needed to have such representations.

引用

页码：3083 / 3107

页数：25

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