Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
Book Information:

Author: A. A. Karatsuba and S. M. Voronin
Title: The Riemann zeta function
Additional book information: de Gruyter, Berlin and Hawthorne, New York, 1991, xii + 396 pp., US$112.00. ISBN 3-11-013170-6.

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

  • [B] E. Bombieri, Le grand crible dans la theorie analytique des nombres, Astérisque 18 (1974). MR 0371840 (51:8057)
  • [B-I] E. Bombieri and H. Iwaniec, On the order of $ {\zeta (\tfrac{1}{2} + it)}$ hypergeometric function with p-adic parameters, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) XIII (1986), 449-472. MR 881101 (88i:11054a)
  • [C] B. Conrey, More than 2/5 of the zeros of the Riemann zeta function are on the critical line, J. Reine Angew. Math 399 (1989), 1-26. MR 1004130 (90g:11120)
  • [Da] H. Davenport, Multiplicative number theory, Graduate Texts in Math, vol. 74, Springer, New York, 1980. MR 606931 (82m:10001)
  • [D] F. Dyson, Statistical theory of the energy levels of complex systems. III, J. Math. Phys. 3 (1962), 166-175. MR 0143558 (26:1113)
  • [E] H. Edwards, Riemann's zeta function, Academic Press, New York and London, 1974. MR 0466039 (57:5922)
  • [HE] D. R. Heath-Brown, The twelfth power moment of the Riemann zeta-function, Quart. J. Math. Oxford Ser. (2) 29 (1978), 443-462. MR 517737 (80d:10059)
  • [H] M. Huxley, The distribution of prime numbers, Oxford Univ. Press, London, 1972. MR 0444593 (56:2943)
  • [IV] A. Ivic, The distribution of prime numbers, Oxford Univ. Press, London, 1985.
  • [I] H. Iwaniec, Fourier coefficients of cusp forms and the Riemann zeta function, Sém. Théor. Nombres Bordeaux (2), vol. 18, Univ. Bordeaux, Talence, 1980. MR 604215 (82i:10047)
  • [J] M. Jutila, Zero density estimates for L-functions, Acta Arith. 32 (1977), 52-62. MR 0429790 (55:2800)
  • [ME] M. L. Mehta, Random matrices, second ed., Academic Press, New York, 1991. MR 1083764 (92f:82002)
  • [MO1] H. Montgomery, The pair correlation of zeros of the zeta function, Proc. Sympos. Pure Math., vol. XXIV, Amer. Math. Soc., Providence, RI, 1973, pp. 181-193. MR 0337821 (49:2590)
  • [MO2] -, Topics in multiplicative number theory, Lecture Notes in Math., vol. 227, Springer, New York, 1971. MR 0337847 (49:2616)
  • [O] A. Odlyzko, The distribution of spacings between zeros of the zeta function, Math. Comp. 48 (1987), 273-308. MR 866115 (88d:11082)
  • [S] A. Selberg, Old and new conjectures about a class of Dirichlet series, Collected Work, Vol. II, Springer, New York, 1991, pp. 47-65.
  • [TI] E. C. Titchmarsh, The theory of the Riemann zeta function, Oxford Univ. Press, London, 1951. MR 0046485 (13:741c)
  • [T2] -, The theory of the Riemann zeta function, second ed. rev. D. R. Heath-Brown, Oxford Univ. Press, London, 1986. MR 882550 (88c:11049)

Review Information:

Reviewer: Peter Sarnak
Journal: Bull. Amer. Math. Soc. 32 (1995), 251-253
American Mathematical Society