On the WaringGoldbach problem for seventh powers
Author:
Angel V. Kumchev
Journal:
Proc. Amer. Math. Soc. 133 (2005), 29272937
MSC (2000):
Primary 11P32, 11L20, 11N36, 11P05, 11P55
Published electronically:
April 25, 2005
MathSciNet review:
2159771
Fulltext PDF Free Access
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References 
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Additional Information
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.
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 A. Kumchev, On the WaringGoldbach problem. Exceptional sets for sums of cubes and higher powers, to appear in Canad. J. Math.
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 , On Weyl sums over primes and almost primes, preprint.
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 J. Y. Liu and T. Zhan, The exceptional set in Hua's theorem for three squares of primes, to appear in Acta. Math. Sinica.
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 K. Thanigasalam, Improvement on Davenport's iterative method and new results in additive number theory I, Acta Arith. 46 (1985), 131. MR 0831261 (87e:11118)
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 , Improvement on Davenport's iterative method and new results in additive number theory III, Acta Arith. 48 (1987), 97116. MR 0895435 (88f:11097)
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 , On admissible exponents for th powers, Bull. Calcutta Math. Soc. 86 (1994), 175178. MR 1323498 (96c:11117)
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 R. C. Vaughan, On Waring's problem for smaller exponents, Proc. London Math. Soc. (3) 52 (1986), 445463. MR 0833645 (87g:11126)
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 , The HardyLittlewood Method, second ed., Cambridge Tracts Math., vol. 125, Cambridge University Press, Cambridge, 1997. MR 1435742 (98a:11133)
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 I. M. Vinogradov, Representation of an odd number as the sum of three primes, Dokl. Akad. Nauk SSSR 15 (1937), 291294, in Russian.
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Additional Information
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:
http://dx.doi.org/10.1090/S0002993905079086
PII:
S 00029939(05)079086
Received by editor(s):
May 17, 2004
Received by editor(s) in revised form:
June 10, 2004
Published electronically:
April 25, 2005
Communicated by:
WenChing Winnie Li
Article copyright:
© Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
