On the Waring-Goldbach problem for fourth and fifth powers

Proceedings of the London Mathematical Society

Volumn 83, Issue 1, 2001, Pages 1-50

  Kawada, Koichi ^a   Wooley, Trevor D ^b  

^a IWATE UNIVERSITY   (Japan)

^b UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002426593     PISSN: 00246115     EISSN: None     Source Type: Journal    
DOI: 10.1112/plms/83.1.1     Document Type: Article

References (21)

1. J. BRÜDERN, 'Sieves, the circle method, and Waring's problem for cubes' (Habilitationschrift, Göttingen 1991), Mathematica Gottingensis 51 (1991).
2. J. BRÜDERN, 'A sieve approach to the Waring-Goldbach problem, I: sums of four cubes', Ann. Sci. École Norm. Sup. (4) 28 (1995) 461-476.
3. J. BRÜDERN, 'A sieve approach to the Waring-Goldbach problem, II. On the seven cubes theorem', Acta Arith. 72 (1995) 211-227.
4. H. DAVENPORT, 'On Waring's problem for fourth powers', Ann. of Math. 40 (1939) 731-747.
5. D. R. HEATH-BROWN, 'Three primes and an almost-prime in arithmetic progression', J. London Math. Soc. (2) 23 (1981) 396-414.
6. L.-K. HUA, 'On the representation of numbers as the sums of the powers of primes', Math. Z. 44 (1938) 335-346.
7. L.-K. HUA, Abschätzungen von Exponentialsummen und ihre Anwendung in der Zahlentheorie, Enzyklopädie der Mathematischen Wissenschaften, Band I 2, Heft 13, Teil 1 (Teubner, Leipzig, 1959).
8. L.-K. HUA, Additive theory of prime numbers (American Mathematical Society, Providence, RI, 1965).
9. H. IWANIEC, 'A new form of the error term in the linear sieve', Acta Arith. 37 (1980) 307-320.
10. K. KAWADA, 'Note on the sum of cubes of primes and an almost prime', Arch. Math. (Basel) 69 (1997) 13-19.
11. K. THANIGASALAM, 'Improvement on Davenport's iterative method and new results in additive number theory, I', Acta Arith. 46 (1985) 1-31.
12. K. THANIGASALAM, 'Improvement on Davenport's iterative method and new results in additive number theory, II. Proof that G(5) ≤ 22', Acta Arith. 46 (1986) 91-112.
13. K. THANIGASALAM, 'Improvement on Davenport's iterative method and new results in additive number theory, III', Acta Arith. 48 (1987) 97-116.
14. K. THANIGASALAM, 'On sums of positive integral powers and simple proof of G(6) ≤ 31', Bull. Calcutta Math. Soc. 81 (1989) 279-294.
15. K. THANIGASALAM, 'On admissible exponents for k th powers', Bull. Calcutta Math. Soc. 86 (1994) 175-178.
16. R. C. VAUGHAN, 'Recent work in additive prime number theory', Proceedings of the International Congress of Mathematicians, Helsinki, 1978 (Acad. Sci. Fennica, Helsinki, 1980) 389-394.
17. R. C. VAUGHAN, 'On Waring's problem for smaller exponents', Proc. London Math. Soc. (3) 52 (1986) 445-463.
18. R. C. VAUGHAN, 'A new iterative method in Waring's problem', Acta Math. 162 (1989) 1-71.
19. R. C. VAUGHAN, The Hardy-Littlewood method, 2nd edn (Cambridge University Press, 1997).
20. I. M. VINOGRADOV, 'Representation of an odd number as a sum of three primes', C. R. Acad. Sci. URSS 15 (1937) 6-7.
21. I. M. VINOGRADOV, 'Some theorems concerning the theory of primes', Rec. Math. 2 (1937) 179-195.