American Mathematical Society

Book Review

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

MathSciNet review: 3497796
Full text of review: PDF This review is available free of charge.
Book Information:

Author: H. Iwaniec
Title: Lectures on the Riemann zeta function
Additional book information: University Lecture Series, Vol. 62, American Mathematical Society, Providence, RI, 2014, viii+119 pp., ISBN 978-1-4704-1851, List price US$40, Member price US$32

References

Jonathan Bober, http://www.maths.bris.ac.uk/˜jb12407/

J. B. Conrey, D. W. Farmer, J. P. Keating, M. O. Rubinstein, and N. C. Snaith, Integral moments of $L$-functions, Proc. London Math. Soc. (3) 91 (2005), no. 1, 33–104. MR 2149530, DOI https://doi.org/10.1112/S0024611504015175

Brian Conrey, David W. Farmer, and Martin R. Zirnbauer, Autocorrelation of ratios of $L$-functions, Commun. Number Theory Phys. 2 (2008), no. 3, 593–636. MR 2482944, DOI https://doi.org/10.4310/CNTP.2008.v2.n3.a4

J. B. Conrey and N. C. Snaith, Applications of the $L$-functions ratios conjectures, Proc. Lond. Math. Soc. (3) 94 (2007), no. 3, 594–646. MR 2325314, DOI https://doi.org/10.1112/plms/pdl021

David W. Farmer, Sally Koutsoliotas, and Stefan Lemurell, Maass forms on ${\rm GL}(3)$ and ${\rm GL}(4)$, Int. Math. Res. Not. IMRN 22 (2014), 6276–6301. MR 3283005, DOI https://doi.org/10.1093/imrn/rnt145

Ghaith Ayesh Hiary, Fast methods to compute the Riemann zeta function, Ann. of Math. (2) 174 (2011), no. 2, 891–946. MR 2831110, DOI https://doi.org/10.4007/annals.2011.174.2.4

Nicholas M. Katz and Peter Sarnak, Zeroes of zeta functions and symmetry, Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 1, 1–26. MR 1640151, DOI https://doi.org/10.1090/S0273-0979-99-00766-1

J. P. Keating and N. C. Snaith, Random matrix theory and $\zeta (1/2+it)$, Comm. Math. Phys. 214 (2000), no. 1, 57–89. MR 1794265, DOI https://doi.org/10.1007/s002200000261

Norman Levinson, More than one third of zeros of Riemann’s zeta-function are on $\sigma =1/2$, Advances in Math. 13 (1974), 383–436. MR 564081, DOI https://doi.org/10.1016/0001-8708%2874%2990074-7

The L-functions and modular forms database, http://www.lmfdb.org/

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

Atle Selberg, On the zeros of Riemann’s zeta-function, Skr. Norske Vid.-Akad. Oslo I 1942 (1942), no. 10, 59. MR 10712

Review Information:

Reviewer: Brian Conrey
Affiliation: American Institute of Mathematics, San Jose, California; and University of Bristol, United Kingdom
Email: conrey@aimath.org