Book Review
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MathSciNet review:
1568166
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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.
Enrico Bombieri, Le grand crible dans la théorie analytique des nombres, Astérisque, No. 18, Société Mathématique de France, Paris, 1974 (French). Avec une sommaire en anglais. MR 0371840
E. Bombieri and H. Iwaniec, On the order of $\zeta ({1\over 2}+it)$, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 13 (1986), no. 3, 449–472. MR 881101
J. B. Conrey, More than two fifths of the zeros of the Riemann zeta function are on the critical line, J. Reine Angew. Math. 399 (1989), 1–26. MR 1004130, DOI 10.1515/crll.1989.399.1
Harold Davenport, Multiplicative number theory, 2nd ed., Graduate Texts in Mathematics, vol. 74, Springer-Verlag, New York-Berlin, 1980. Revised by Hugh L. Montgomery. MR 606931
Freeman J. Dyson, Statistical theory of the energy levels of complex systems. III, J. Mathematical Phys. 3 (1962), 166–175. MR 143558, DOI 10.1063/1.1703775
H. M. Edwards, Riemann’s zeta function, Pure and Applied Mathematics, Vol. 58, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. MR 0466039
D. R. Heath-Brown, The twelfth power moment of the Riemann-function, Quart. J. Math. Oxford Ser. (2) 29 (1978), no. 116, 443–462. MR 517737, DOI 10.1093/qmath/29.4.443
M. N. Huxley, The distribution of prime numbers, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1972. Large sieves and zero-density theorems. MR 0444593
[IV] A. Ivic, The distribution of prime numbers, Oxford Univ. Press, London, 1985.
Henryk Iwaniec, Fourier coefficients of cusp forms and the Riemann zeta-function, Seminar on Number Theory, 1979–1980 (French), Univ. Bordeaux I, Talence, 1980, pp. Exp. No. 18, 36. MR 604215
Matti Jutila, Zero-density estimates for $L$-functions, Acta Arith. 32 (1977), no. 1, 55–62. MR 429790, DOI 10.4064/aa-32-1-55-62
Madan Lal Mehta, Random matrices, 2nd ed., Academic Press, Inc., Boston, MA, 1991. MR 1083764
H. L. Montgomery, The pair correlation of zeros of the zeta function, Analytic number theory (Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972) Amer. Math. Soc., Providence, R.I., 1973, pp. 181–193. MR 0337821
Hugh L. Montgomery, Topics in multiplicative number theory, Lecture Notes in Mathematics, Vol. 227, Springer-Verlag, Berlin-New York, 1971. MR 0337847
A. M. Odlyzko, On the distribution of spacings between zeros of the zeta function, Math. Comp. 48 (1987), no. 177, 273–308. MR 866115, DOI 10.1090/S0025-5718-1987-0866115-0
[S] A. Selberg, Old and new conjectures about a class of Dirichlet series, Collected Work, Vol. II, Springer, New York, 1991, pp. 47-65.
E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford, at the Clarendon Press, 1951. MR 0046485
E. C. Titchmarsh, The theory of the Riemann zeta-function, 2nd ed., The Clarendon Press, Oxford University Press, New York, 1986. Edited and with a preface by D. R. Heath-Brown. MR 882550
- [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
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
DOI:
https://doi.org/10.1090/S0273-0979-1995-00580-X
