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On the Waring–Goldbach problem for fourth and sixth powers
Author(s) -
Zhao Lilu
Publication year - 2014
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdt072
Subject(s) - goldbach's conjecture , mathematics , congruence (geometry) , sums of powers , prime number , prime (order theory) , number theory , combinatorics , arithmetic , mathematics education , geometry
We consider the Waring–Goldbach problem for fourth and sixth powers. In particular, we establish that every sufficiently large positive integer under a natural congruence condition can be represented as a sum of 13 fourth powers of prime numbers. This improves upon the earlier result of Kawada and Wooley [‘On the Waring–Goldbach problem for fourth and fifth powers’, Proc. London Math. Soc . (3) 83 (2001) 1–50].