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Bulletin of the American Mathematical Society

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Book Review

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Book Information:

Author: R. C. Vaughan
Title: The Hardy-Littlewood method
Additional book information: Cambridge Tracts in Mathematics, vol. 80, Cambridge University Press, Cambridge, 1981, xii + 172 pp., $34.50.

References [Enhancements On Off] (What's this?)

  • 1. B. J. Birch [1957], Homogeneous forms of odd degree in a large number of variables, Mathematika 4, 102-105. MR 97359
  • 2. H. Davenport [1962], Analytic methods for diophantine equations and diophantine inequalities, Univ. of Michigan, Fall semester 1962, Campus Publishers. MR 2152164
  • 3. H. Davenport [1963], Cubic forms in 16 variables, Proc. Roy. Soc. Ser. A 272, 285-303. MR 155800
  • 4. H. Davenport and H. Heilbronn [1946], On indefinite quadratic forms in five variables, J. London Math. Soc. (2) 21, 185-193. MR 20578
  • 5. H. Davenport and D. J. Lewis [1969], Simultaneous equations of additive type, Philos. Trans. Roy. Soc. London Ser. A 264, 557-595. MR 245542
  • 6. M. J. Greenberg [1969], Lectures on forms in many variables, Benjamin, New York and Amsterdam. MR 241358
  • 7. G. H. Hardy and J. E. Littlewood [1919], A new solution of Waring's problem, Quart. J. Math. 48, 272-293. (See also Hardy's collected papers, vol. I, Clarendon Press, Oxford, 1966, pp. 382-403.)
  • 8. G. H. Hardy and S. Ramanujan [1918], Asymptotic formulae in combinatory analysis, Proc. London Math. Soc. (2) 17, 75-115.
  • 9. D. Hilbert [1909], Beweis für die Darstellbarkeit der ganzen Zahlen durch eine feste Anzahl n-ter Potenzen (Waringsches Problem), Göttinger Nachrichten, 17-36.
  • 10. C. Hooley [1981], On a new approach to various problems of Waring's type, Recent Progress in Analytic Number Theory (Sympos., Durham, July 1979), Academic Press, New York, pp. 127-191. MR 637346
  • 11. L. K. Hua [1938], On Waring's problem, Quart. J. Math. 9, 199-202.
  • 12. J. I. Igusa [1978], Lectures on forms of higher degree, Tata Inst. Fundamental Research, Bombay. MR 546292
  • 13. Yu. V. Linnik [1960], All large numbers are sums of a prime and two squares (A problem of Hardy and Littlewood). I, Mat. Sb. (N.S.) 52 (94), 661-700. (Russian) MR 120206
  • 14. W. M. Schmidt [1980], Diophantine inequalities for forms of odd degree, Adv. in Math. 38, 128-151. MR 597195
  • 15. W. M. Schmidt [to appear], On cubic polynomials. II-IV; Monatsh. Math. Part I 93 (1982), 63-74. MR 648740
  • 16. I. M. Vinogradov [1928], Sur le théorème de Waring, C. R. Acad. Sci. USSR, 393-400.
  • 17. I. M. Vinogradov [1937], Representation of an odd number as a sum of three primes, C. R. Acad. Sci. USSR 15, 6-7.
  • 18. I. M. Vinogradov [1947], The method of trigonometrical sums in the theory of numbers, "Nauka" Interscience, New York. MR 29417
  • 19. I. M. Vinogradov [1971], The method of trigonometrical sums in the theory of numbers, Moscow. (Russian) MR 409380
  • 20. H. Weyl [1916], Über die Gleichverteilung von Zahlen mod Eins, Math. Ann. 77, 313-352. MR 1511862

Review Information:

Reviewer: Wolfgang M. Schmidt
Journal: Bull. Amer. Math. Soc. 7 (1982), 433-437
DOI: https://doi.org/10.1090/S0273-0979-1982-15059-5
American Mathematical Society