Waring-Goldbach Problem for Unlike Powers

In this paper, the authors investigate exceptional sets in the Waring-Goldbach problem for unlike powers. For example, estimates are obtained for sufficiently large integers below a parameter subject to the necessary local conditions that do not have a representation as the sum of a square of prime,...

Full description

Saved in:
Bibliographic Details
Published inChinese annals of mathematics. Serie B Vol. 46; no. 2; pp. 303 - 320
Main Authors Feng, Zhenzhen, Ma, Jing
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2025
Springer Nature B.V
Subjects
Applications of Mathematics
Estimates
Mathematics
Mathematics and Statistics
Exceptional sets
Waring-Goldbach problem
Circle method
11P55
11P32
Online AccessGet full text

Cover

More Information
Summary:In this paper, the authors investigate exceptional sets in the Waring-Goldbach problem for unlike powers. For example, estimates are obtained for sufficiently large integers below a parameter subject to the necessary local conditions that do not have a representation as the sum of a square of prime, a cube of prime and a sixth power of prime and a k -th power of prime. These results improve the recent result due to Brüdern in the order of magnitude. Furthermore, the method can be also applied to the similar estimates for the exceptional sets for Waring-Goldbach problem for unlike powers.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0252-9599
1860-6261
DOI:10.1007/s11401-025-0017-0