Proceedings of the American Mathematical Society

Author(s): Angel V. Kumchev
Journal: Proc. Amer. Math. Soc. 133 (2005), 2927-2937.
MSC (2000): Primary 11P32, 11L20, 11N36, 11P05, 11P55
Posted: April 25, 2005
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Abstract: We use sieve theory and recent estimates for Weyl sums over almost primes to prove that every sufficiently large even integer is the sum of

seventh powers of prime numbers.

1.: H. Davenport, Multiplicative Number Theory, third ed., Graduate Texts in Mathematics, vol. 74, Springer-Verlag, New York, 2000, revised by H. L. Montgomery. MR 1790423 (2001f:11001)
2.: N. J. de Bruijn, On the number of uncancelled elements in the sieve of Eratosthenes, Proc. Kon. Ned. Akad. Wetensch. 53 (1950), 803-812. MR 0035785 (12:11d)
3.: G. Harman, On the distribution of $\alpha p$ modulo one II, Proc. London Math. Soc. (3) 72 (1996), 241-260. MR 1367078 (96k:11089)
4.: L. K. Hua, Some results in prime number theory, Quart. J. Math. Oxford Ser. 9 (1938), 68-80.
5.: -, Additive Theory of Prime Numbers, American Mathematical Society, Providence, RI, 1965. MR 0194404 (33:2614)
6.: A. E. Ingham, The Distribution of Primes, reprint of the 1932 original ed., Cambridge University Press, Cambridge, 1990, with a foreword by R. C. Vaughan. MR 1074573 (91f:11064)
7.: K. Kawada and T. D. Wooley, On the Waring-Goldbach problem for fourth and fifth powers, Proc. London Math. Soc. (3) 83 (2001), 1-50. MR 1829558 (2002b:11134)
8.: A. Kumchev, On the Waring-Goldbach problem. Exceptional sets for sums of cubes and higher powers, to appear in Canad. J. Math.
9.: -, On Weyl sums over primes and almost primes, preprint.
10.: J. Y. Liu and T. Zhan, The exceptional set in Hua's theorem for three squares of primes, to appear in Acta. Math. Sinica.
11.: K. Thanigasalam, Improvement on Davenport's iterative method and new results in additive number theory I, Acta Arith. 46 (1985), 1-31. MR 0831261 (87e:11118)
12.: -, Improvement on Davenport's iterative method and new results in additive number theory III, Acta Arith. 48 (1987), 97-116. MR 0895435 (88f:11097)
13.: -, On admissible exponents for th powers, Bull. Calcutta Math. Soc. 86 (1994), 175-178. MR 1323498 (96c:11117)
14.: R. C. Vaughan, On Waring's problem for smaller exponents, Proc. London Math. Soc. (3) 52 (1986), 445-463. MR 0833645 (87g:11126)
15.: -, The Hardy-Littlewood Method, second ed., Cambridge Tracts Math., vol. 125, Cambridge University Press, Cambridge, 1997. MR 1435742 (98a:11133)
16.: I. M. Vinogradov, Representation of an odd number as the sum of three primes, Dokl. Akad. Nauk SSSR 15 (1937), 291-294, in Russian.

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11P32, 11L20, 11N36, 11P05, 11P55

Angel V. Kumchev
Affiliation: Department of Mathematics, 1 University Station, C1200, The University of Texas at Austin, Austin, Texas 78712
Email: kumchev@math.utexas.edu

DOI: 10.1090/S0002-9939-05-07908-6
PII: S 0002-9939(05)07908-6
Received by editor(s): May 17, 2004
Received by editor(s) in revised form: June 10, 2004
Posted: April 25, 2005
Communicated by: Wen-Ching Winnie Li
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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