The application of a new mean value theorem to the fractional parts of polynomials

• Autorzy: Trevor D. Wooley
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1993
• Tom: 65
• Numer: 2
• Strony: 163-179

Daty

wydano

1993

otrzymano

1993-01-18

Twórcy

autor

Trevor D. Wooley

• Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1003, U.S.A.

Bibliografia

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• [3] I. Danicic, Contributions to Number Theory, Ph.D. Thesis, London, 1957.
• [4] G. Harman, Trigonometric sums over primes I, Mathematika 28 (1981), 249-254.
• [5] D. R. Heath-Brown, On the fractional part of $αn^k$, Mathematika 35 (1988), 28-37.
• [6] H. Heilbronn, On the distribution of the sequence n²θ (mod 1), Quart. J. Math. Oxford 19 (1948), 249-256.
• [7] K. Thanigasalam, Some new estimates for G(k) in Waring's problem, Acta Arith. 42 (1982), 73-78.
• [8] R. C. Vaughan, The Hardy-Littlewood Method, Cambridge Tracts Math. 80, Cambridge Univ. Press, 1981.
• [9] R. C. Vaughan, A new iterative method in Waring's problem, Acta Math. 162 (1989), 1-71.
• [10] R. C. Vaughan, A new iterative method in Waring's problem, II, J. London Math. Soc. (2) 39 (1989), 219-230.
• [11] R. C. Vaughan and T. D. Wooley, Further improvements in Waring's problem, to appear.
• [12] I. M. Vinogradov, Analytischer Beweis des Satzes über die Verteilung der Bruch- teile eines ganzen Polynoms, Bull. Acad. Sci. USSR (6) 21 (1927), 567-578.
• [13] H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352.
• [14] T. D. Wooley, Large improvements in Waring's problem, Ann. of Math. 135 (1992), 131-164.