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Book Review
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Book Information
Author(s):
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:
- [B]
- E. Bombieri, Le grand crible dans la theorie analytique des nombres, Ast\'erisque \textbf{18} (1974).
- [B-I]
- E. Bombieri and H. Iwaniec, On the order of $\zeta (\frac 12+it)$ hypergeometric function with $p$-adic parameters, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) \textbf{XIII} (1986), 449--472.
- [C]
- B. Conrey, More than $2/5$ of the zeros of the Riemann zeta function are on the critical line, J. Reine Angew. Math \textbf{399} (1989), 1--26.
- [Da]
- H. Davenport, Multiplicative number theory, Graduate Texts in Math, vol. 74, Springer, New York, 1980.
- [D]
- F. Dyson, Statistical theory of the energy levels of complex systems. \rm III, J. Math. Phys. \textbf{3} (1962), 166--175.
- [E]
- H. Edwards, Riemann\RM 's zeta function, Academic Press, New York and London, 1974.
- [HE]
- D. R. Heath-Brown, The twelfth power moment of the Riemann zeta-function, Quart. J. Math. Oxford Ser. (2) \textbf{29} (1978), 443--462.
- [H]
- M. Huxley, The distribution of prime numbers, Oxford Univ. Press, London, 1972.
- [IV]
- A. Ivic, The distribution of prime numbers, Oxford Univ. Press, London, 1985.
- [I]
- H. Iwaniec, \emph{Fourier coefficients of cusp forms and the Riemann zeta function}, Univ. Bordeaux, Talence, 1980.
- [J]
- M. Jutila, Zero density estimates for $L$-functions, Acta Arith. \textbf{32} (1977), 52--62.
- [ME]
- M. L. Mehta, Random matrices, second ed., Academic Press, New York, 1991.
- [MO1]
- H. Montgomery, \emph{The pair correlation of zeros of the zeta function}, Amer. Math. Soc., Providence, RI, 1973 pp.~181--193.
- [MO2]
- H. Montgomery, Topics in multiplicative number theory, Lecture Notes in Math., vol.~227, Springer, New York, 1971.
- [O]
- A. Odlyzko, The distribution of spacings between zeros of the zeta function, Math. Comp. \textbf{48} (1987), 273--308.
- [S]
- A. Selberg, Old and new conjectures about a class of Dirichlet series, Collected Work, Vol. \rm II, Springer, New York, 1991, pp.~47--65.
- [TI]
- E. C. Titchmarsh, The theory of the Riemann zeta function, Oxford Univ. Press, London, 1951.
- [T2]
- E. C. Titchmarsh, The theory of the Riemann zeta function, second ed. rev. D. R. Heath-Brown, Oxford Univ. Press, London, 1986.
Additional Information:
Reviewer(s):
Peter
Sarnak
Review Information:
Journal:
Bull. Amer. Math. Soc.
32
(1995),
251-253.
DOI:
10.1090/S0273-0979-1995-00580-X
PII:
S 0273-0979(1995)00580-X
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