On a refinement of waring’s problem

Duke Mathematical Journal

Volumn 105, Issue 1, 2000, Pages 107-134

  Vu, Van H ^a  

^a MICROSOFT   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034666868     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-00-10516-9     Document Type: Article

References (30)

1. 1/3 squares, Proc. Amer. Math. Soc. 79 (1980), 203-205.
2. P. Erdos, “Problems and results in additive number theory” in Colloque sur la Théorie des Nombres (Bruxelles, 1955), Masson and Cie, Paris, 1956, 127-137.
3. P. Erdos and M. Nathanson, “Lagrange's theorem and thin subsequences of squares” in Contribution to Probability, ed. J. Gani and V. K. Rohatgi, Academic Press, New York, 1981, 3-9.
4. P. Erdos and R. Rado, Intersection theorems for systems of sets, J. London Math. Soc. 35 (1960), 85-90.
5. P. Erdos and A. Rényi, Additive properties of random sequences of positive integers, Acta Arith. 6 (1960), 83-110.
6. P. Erdos, A. Sárkozy, and V. T. Sós, Problems and results on additive properties of general sequences, III, Studia Sci. Math. Hungar. 22 (1987), 53-63.
7. P. Erdos and P. Tetali, Representations of integers as the sum ofk terms, Random Structures Algorithms 1 (1990), 245-261.
8. P. Erdos and P. Turán, On a problem of Sidon in additive number theory, and on some related problems, J. London Math. Soc. 16 (1941), 212-215.
9. H. Halberstam and K. F. Roth, Sequences, 2d ed. Springer, New York, 1983.
10. D. Hilbert, Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl unter Potenzen (Waringsche Problem), Nachrichten von der Koniglichen Gesellschaft der Wissenschaften zu Gottingen, mathematisch-physikalische Klasse aus dom Jahr 1909, 17-36; Math. Ann. 67 (1909), 281-300.
11. S. Janson, Poisson approximation for large deviations, Random Structures Algorithms 1 (1990), 221-229.
12. J. H. Kim and V. H. Vu, Concentration of multivariate polynomials and its applications, Combinatorica 20 (2000), 417-434.
13. J. H. Kim and V. H. Vu, Small complete arcs on projective planes, submitted.
14. M. Kolountzakis, “Some applications of probability to additive number theory and harmonic analysis” in Number Theory (New York, 1991-1995), ed. D. V. Chudnovsky, G. V. Chudnovsky, and M. B. Nathanson, Springer, New York, 1996, 229-251.
15. M. Nathanson, “Waring's problem for sets of density zero” in Analytic Number Theory (Philadelphia, 1980), ed. M. Knopp, Lecture Notes in Math. 899, Springer, Berlin, 1981, 301-310.
16. M. Nathanson, Additive Number Theory: The Classical Bases, Grad. Texts in Math. 164, Springer, New York, 1996.
17. C. Pomerance and A. Sárkozy, “Combinatorial number theory” in Handbook of Combinatorics, Vol. 1, ed. R. Graham, M. Grotschel, and L. Lovász, Elsevier, Amsterdam, 1995, 967-1018.
18. I. Ruzsa, A just basis, Monatsh. Math. 109 (1990), 145-151.
19. B. Segre, Legeometrie di Galois, Ann. Mat. Pura Appl. (4) 48 (1959), 1-96.
20. S. Sidon, Ein Satz über trigonomische Polynome und seine Anwendung in der Theorie der Fourier-Reihen, Math. Ann. 106 (1932), 536-539.
21. J. Spencer, “Four squares with few squares” in Number Theory (New York, 1991-1995), ed. D. V. Chudnovsky, G. V Chudnovsky, and M. B. Nathanson, Springer, New York, 1996, 295-297.
22. M. Talagrand, A new look at independence, Ann. Probab. 24 (1996), 1-34.
23. R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts in Math. 80, Cambridge Univ. Press, Cambridge, 1981.
24. V. H. Vu, On some simple degree conditions that guarantee the upper bound on the chromatic (choice) number of random graphs, J. Graph Theory 31 (1999), 201-226.
25. V. H. Vu, On the concentration of multivariate polynomials with small expectation, Random Structures and Algorithms 16 (2000), 344-363.
26. V. H. Vu, New bounds on nearly perfect matchings of hypergraphs: Higher codegrees do help, Random Structures and Algorithms 17 (2000), 29-63.
27. V. H. Vu, Some new concentration results and applications, manuscript.
28. E. Wirsing, Thin subbases, Analysis 6 (1986), 285-308.
29. J. Zollner, Über eine Vermutung von Choi, Erdos und Nathanson, Acta Arith. 45 (1985), 211-213.
30. J. Zollner, Der Vier-Quadrate-Satz und ein Problem von Erdos and Nathanson, Ph.D. thesis, Johannes Gutenberg-Universitat, Mainz, 1984.