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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

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Full text of review: PDF
Book Information:

Author: Gove W. Effinger and David R. Hayes
Title: Additive number theory of polynomials over a finite field
Additional book information: Clarendon Press, Oxford, 157 pp., US$45.00. ISBN 0-19-853583-x.

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

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  • [5] G. H. Hardy and J. E. Littlewood, Some problems of “partitio numerorum”: II. Proof that every large number is the sum of at most 21 biquadrates, Math. Z. 9 (1921), no. 1-2, 14–27. MR 1544448, 10.1007/BF01378332
  • [6] G. H. Hardy and J. E. Littlewood, Some problems of ‘Partitio Numerorum’: IV. The singular series in Waring’s Problem and the value of the number 𝐺(𝑘), Math. Z. 12 (1922), no. 1, 161–188. MR 1544511, 10.1007/BF01482074
  • [7] G. H. Hardy and J. E. Littlewood, Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes, Acta Math. 44 (1923), no. 1, 1–70. MR 1555183, 10.1007/BF02403921
  • [8] -, Some problems of "Partitio Numerorum": V A further contribution to the study of Goldbach's problem, Proc. London Math. Soc. 22 (1923), no. 2, 46-56.
  • [9] G. H. Hardy and J. E. Littlewood, Some problems of ‘Partitio numerorum’ (VI): Further researches in Waring’s Problem, Math. Z. 23 (1925), no. 1, 1–37. MR 1544728, 10.1007/BF01506218
  • [10] -, Some problems of "Partitio Numerorum": VIII The number $ {\Gamma (k)}$ in Waring's problem, Proc. London Math. Soc. 28 (1928), no. 2, 518-542.
  • [11] E. G. H. Landau, Vorlesungen über Zahlentheorie, Verlag von S. Hirzel, Erster Band. Leipzig, 1927
  • [12] R. C. Vaughan, The Hardy-Littlewood method, Cambridge Tracts in Mathematics, vol. 80, Cambridge University Press, Cambridge-New York, 1981. MR 628618
  • [13] I. M. Vinogradov, The method of trigonometrical sums in the theory of numbers, Trav. Inst. Math. Stekloff 23 (1947), 109 (Russian). MR 0029417
  • [14] André Weil, Sur la théorie des formes quadratiques, Colloq. Théorie des Groupes Algébriques (Bruxelles, 1962) Librairie Universitaire, Louvain; Gauthier-Villars, Paris, 1962, pp. 9–22 (French). MR 0190097
  • [15] André Weil, Sur la formule de Siegel dans la théorie des groupes classiques, Acta Math. 113 (1965), 1–87 (French). MR 0223373

Review Information:

Reviewer: R. C. Vaughan
Journal: Bull. Amer. Math. Soc. 28 (1993), 209-212
DOI: http://dx.doi.org/10.1090/S0273-0979-1993-00359-8