On a conjecture of Sun about sums of restricted squares

被引：0

作者：

Banerjee, Soumyarup ^{[1
]}

机构：

[1] Indian Inst Technol Kharagpur, Dept Math, Kharagpur 721302, W Bengal, India

来源：

JOURNAL OF NUMBER THEORY | 2024年 / 256卷

关键词：

Sums of squares; Almost prime numbers; Quadratic forms; Theta function; Sieve theory; THEOREM;

D O I：

10.1016/j.jnt.2023.09.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate sums of four squares of integers whose prime factorizations are restricted, making progress towards a conjecture of Sun that states that two of the integers may be restricted to the forms 2a3b and 2c5d. We obtain an ineffective generalization of results of Gauss and Legendre on sums of three squares and an effective generalization of Lagrange's four-square theorem. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：253 / 289

页数：37

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