Book Review
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MathSciNet review:
3497796
Full text of review:
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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
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 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 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 10.1112/plms/pdl021
David W. Farmer, Sally Koutsoliotas, and Stefan Lemurell, Maass forms on $\textrm {GL}(3)$ and $\textrm {GL}(4)$, Int. Math. Res. Not. IMRN 22 (2014), 6276–6301. MR 3283005, DOI 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 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 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 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 10.1016/0001-8708(74)90074-7
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
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 (2006j:11120), DOI 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 (2009j:11138), DOI 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 (2009a:11179), DOI 10.1112/plms/pdl021
- David W. Farmer, Sally Koutsoliotas, and Stefan Lemurell, Maass forms on $\textrm {GL}(3)$ and $\textrm {GL}(4)$, Int. Math. Res. Not. IMRN 22 (2014), 6276–6301. MR 3283005
- Ghaith Ayesh Hiary, Fast methods to compute the Riemann zeta function, Ann. of Math. (2) 174 (2011), no. 2, 891–946. MR 2831110 (2012g:11154), DOI 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 (2000f:11114), DOI 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 (2002c:11107), DOI 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 0564081 (58 \#27837)
- 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 (49 \#2590)
- Atle Selberg, On the zeros of Riemann’s zeta-function, Skr. Norske Vid. Akad. Oslo I. 1942 (1942), no. 10, 59. MR 0010712 (6,58a)
Review Information:
Reviewer:
Brian Conrey
Affiliation:
American Institute of Mathematics, San Jose, California; and University of Bristol, United Kingdom
Email:
conrey@aimath.org
Journal:
Bull. Amer. Math. Soc.
53 (2016), 507-512
DOI:
https://doi.org/10.1090/bull/1525
Published electronically:
January 14, 2016
Review copyright:
© Copyright 2016
American Mathematical Society