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Book Review
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Book Information
Author(s):
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:
- 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
Additional Information:
Reviewer(s):
Wolfgang M.
Schmidt
Review Information:
Journal:
Bull. Amer. Math. Soc.
7
(1982),
433-437.
DOI:
10.1090/S0273-0979-1982-15059-5
PII:
S 0273-0979(1982)15059-5
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