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: N. Katz
Title: Convolution and equidistribution: Sato-Tate theorems for finite fields Mellin transforms
Additional book information: Annals of Mathematical Studies, 180, Princeton University Press, Princeton, NJ, 2012, viii+203 pages, ISBN 13: 978-0-691-15331-5, US $75.00, cloth

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

  • [1] Pierre Deligne, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137-252 (French). MR 601520 (83c:14017)
  • [2] Manfred Einsiedler, The ergodic theory of lattice subgroups [book review of MR 2573139], Bull. Amer. Math. Soc. (N.S.) 48 (2011), no. 3, 475-480. MR 2816388, https://doi.org/10.1090/S0273-0979-2011-01335-0
  • [3] Ofer Gabber and François Loeser, Faisceaux pervers $ l$-adiques sur un tore, Duke Math. J. 83 (1996), no. 3, 501-606 (French). MR 1390656 (97i:14016), https://doi.org/10.1215/S0012-7094-96-08317-9
  • [4] Henryk Iwaniec, Topics in classical automorphic forms, Graduate Studies in Mathematics, vol. 17, American Mathematical Society, Providence, RI, 1997. MR 1474964 (98e:11051)
  • [5] Henryk Iwaniec and Emmanuel Kowalski, Analytic number theory, American Mathematical Society Colloquium Publications, vol. 53, American Mathematical Society, Providence, RI, 2004. MR 2061214 (2005h:11005)
  • [6] Nicholas M. Katz, Gauss sums, Kloosterman sums, and monodromy groups, Annals of Mathematics Studies, vol. 116, Princeton University Press, Princeton, NJ, 1988. MR 955052 (91a:11028)
  • [7] Nicholas M. Katz, Exponential sums over finite fields and differential equations over the complex numbers: some interactions, Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 2, 269-309. MR 1032857 (91d:11067), https://doi.org/10.1090/S0273-0979-1990-15922-1
  • [8] Nicholas M. Katz, Exponential sums and differential equations, Annals of Mathematics Studies, vol. 124, Princeton University Press, Princeton, NJ, 1990. MR 1081536 (93a:14009)
  • [9] Nicholas M. Katz, Moments, monodromy, and perversity: a Diophantine perspective, Annals of Mathematics Studies, vol. 159, Princeton University Press, Princeton, NJ, 2005. MR 2183396 (2006j:14020)
  • [10] Nicholas M. Katz and Peter Sarnak, Random matrices, Frobenius eigenvalues, and monodromy, American Mathematical Society Colloquium Publications, vol. 45, American Mathematical Society, Providence, RI, 1999. MR 1659828 (2000b:11070)
  • [11] Pär Kurlberg and Zeév Rudnick, On the distribution of matrix elements for the quantum cat map, Ann. of Math. (2) 161 (2005), no. 1, 489-507. MR 2150390 (2006h:81091), https://doi.org/10.4007/annals.2005.161.489
  • [12] Pär Kurlberg, Lior Rosenzweig, and Zeév Rudnick, Matrix elements for the quantum cat map: fluctuations in short windows, Nonlinearity 20 (2007), no. 10, 2289-2304. MR 2356110 (2008k:81117), https://doi.org/10.1088/0951-7715/20/10/001
  • [13] Alexander Lubotzky, Expander graphs in pure and applied mathematics, Bull. Amer. Math. Soc. (N.S.) 49 (2012), no. 1, 113-162. MR 2869010 (2012m:05003), https://doi.org/10.1090/S0273-0979-2011-01359-3
  • [14] Barry Mazur, Finding meaning in error terms, Bull. Amer. Math. Soc. (N.S.) 45 (2008), no. 2, 185-228. MR 2383303 (2009c:11083), https://doi.org/10.1090/S0273-0979-08-01207-X
  • [15] Peter Sarnak, Spectra of hyperbolic surfaces, Bull. Amer. Math. Soc. (N.S.) 40 (2003), no. 4, 441-478. MR 1997348 (2004f:11107), https://doi.org/10.1090/S0273-0979-03-00991-1
  • [16] J-P. Serre: Inaugural Minerva Lecture, ``Equidistribution'', https:www.math.princeton.edu/
    events/seminars/minerva-lectures/inaugural-minerva-lectures-i-equidistribution
  • [17] Tamás Szamuely, Galois groups and fundamental groups, Cambridge Studies in Advanced Mathematics, vol. 117, Cambridge University Press, Cambridge, 2009. MR 2548205 (2011b:14064)
  • [18] H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1914).

Review Information:

Reviewer: Emmanuel Kowalski
Affiliation: ETH Zürich – D-MATH Rämistrasse 101, CH-8092 Zürich, Switzerland
Email: kowalski@math.ethz.ch
Journal: Bull. Amer. Math. Soc. 51 (2014), 141-149
MSC (2010): Primary 11Txx, 20Gxx, 14Fxx
DOI: https://doi.org/10.1090/S0273-0979-2013-01412-5
Published electronically: June 10, 2013
Review copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
American Mathematical Society