Book Review
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MathSciNet review:
1568019
Full text of review:
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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.
[1] H. Davenport, Analytic methods for diophantine equations and inequalities, Ann Arbor Publ., Ann Arbor, 1962.
[2] -, The collected works of Harold Davenport, vol. III (B. J. Birch, H. Halberstam, and C. A. Rogers, eds.), Academic Press, London, 1977.
[3] G. H. Hardy and J. E. Littlewood, A new solution of Waring's problem, Quart. J. Math. 48 (1919), 272-293.
[4] -, Some problems of "Partitio Numerorum". I A new solution of Waring's problem, Göttingen Nachr., 1920, 33-54.
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, DOI 10.1007/BF01378332
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, DOI 10.1007/BF01482074
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, DOI 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.
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, DOI 10.1007/BF01506218
[10] -, Some problems of "Partitio Numerorum": VIII The number 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
R. C. Vaughan, The Hardy-Littlewood method, Cambridge Tracts in Mathematics, vol. 80, Cambridge University Press, Cambridge-New York, 1981. MR 628618
I. M. Vinogradov, The method of trigonometrical sums in the theory of numbers, Trav. Inst. Math. Stekloff 23 (1947), 109 (Russian). MR 0029417
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
André Weil, Sur la formule de Siegel dans la théorie des groupes classiques, Acta Math. 113 (1965), 1–87 (French). MR 223373, DOI 10.1007/BF02391774
- [1]
- H. Davenport, Analytic methods for diophantine equations and inequalities, Ann Arbor Publ., Ann Arbor, 1962.
- [2]
- -, The collected works of Harold Davenport, vol. III (B. J. Birch, H. Halberstam, and C. A. Rogers, eds.), Academic Press, London, 1977.
- [3]
- G. H. Hardy and J. E. Littlewood, A new solution of Waring's problem, Quart. J. Math. 48 (1919), 272-293.
- [4]
- -, Some problems of "Partitio Numerorum". I A new solution of Waring's problem, Göttingen Nachr., 1920, 33-54.
- [5]
- -, Some problems of "Partitio Numerorum": II Proof that every large number is the sum of at most 21 biquadrates, Math. Z. 9 (1921), 14-27. MR 1544448
- [6]
- -, Some problems of "Partitio Numerorum": IV The singular series in Waring's problem, Math. Z. 12 (1922), 161-188. MR 1544511
- [7]
- -, Some problems of "Partitio Numerorum": III On the expression of a number as a sum of primes, Acta Math. 44 (1923), 1-70. MR 1555183
- [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]
- -, Some problems of "Partitio Numerorum": VI Further researches in Waring's problem, Math. Z. 23 (1925), 1-37. MR 1544728
- [10]
- -, Some problems of "Partitio Numerorum": VIII The number 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 Univ. Press, Cambridge, 1981. MR 628618 (84b:10002)
- [13]
- I. M. Vinogradov, The method of trigonometrical sums in the theory of number, Trav. Inst. Steklov 23 (1947); translated from the Russian, revised, and annotated by A. Davenport and K. F. Roth, Interscience, New York, 1954. MR 0029417 (10:599a)
- [14]
- A. Weil, Sur la théorie des formes quadratiqes, Colloque sur la Théorie des Groupes Algébriques, C. B. R. M. Brussels, 1962, pp. 9-22. MR 0190097 (32:7511)
- [15]
- -, Sur la formula de Siegel dans la théorie des groupes classiques, Acta Math. 113 (1965), 1-87. MR 0223373 (36:6421)
Review Information:
Reviewer:
R. C. Vaughan
Journal:
Bull. Amer. Math. Soc.
28 (1993), 209-212
DOI:
https://doi.org/10.1090/S0273-0979-1993-00359-8