Book Review
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MathSciNet review:
3119825
Full text of review:
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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
Pierre Deligne, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137–252 (French). MR 601520
Manfred Einsiedler, The ergodic theory of lattice subgroups [book review of MR2573139], Bull. Amer. Math. Soc. (N.S.) 48 (2011), no. 3, 475–480. MR 2816388, DOI 10.1090/S0273-0979-2011-01335-0
Ofer Gabber and François Loeser, Faisceaux pervers $l$-adiques sur un tore, Duke Math. J. 83 (1996), no. 3, 501–606 (French). MR 1390656, DOI 10.1215/S0012-7094-96-08317-9
Henryk Iwaniec, Topics in classical automorphic forms, Graduate Studies in Mathematics, vol. 17, American Mathematical Society, Providence, RI, 1997. MR 1474964, DOI 10.1090/gsm/017
Henryk Iwaniec and Emmanuel Kowalski, Analytic number theory, American Mathematical Society Colloquium Publications, vol. 53, American Mathematical Society, Providence, RI, 2004. MR 2061214, DOI 10.1090/coll/053
Nicholas M. Katz, Gauss sums, Kloosterman sums, and monodromy groups, Annals of Mathematics Studies, vol. 116, Princeton University Press, Princeton, NJ, 1988. MR 955052, DOI 10.1515/9781400882120
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, DOI 10.1090/S0273-0979-1990-15922-1
Nicholas M. Katz, Exponential sums and differential equations, Annals of Mathematics Studies, vol. 124, Princeton University Press, Princeton, NJ, 1990. MR 1081536, DOI 10.1515/9781400882434
Nicholas M. Katz, Moments, monodromy, and perversity: a Diophantine perspective, Annals of Mathematics Studies, vol. 159, Princeton University Press, Princeton, NJ, 2005. MR 2183396
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, DOI 10.1090/coll/045
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, DOI 10.4007/annals.2005.161.489
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, DOI 10.1088/0951-7715/20/10/001
Alexander Lubotzky, Expander graphs in pure and applied mathematics, Bull. Amer. Math. Soc. (N.S.) 49 (2012), no. 1, 113–162. MR 2869010, DOI 10.1090/S0273-0979-2011-01359-3
Barry Mazur, Finding meaning in error terms, Bull. Amer. Math. Soc. (N.S.) 45 (2008), no. 2, 185–228. MR 2383303, DOI 10.1090/S0273-0979-08-01207-X
Peter Sarnak, Spectra of hyperbolic surfaces, Bull. Amer. Math. Soc. (N.S.) 40 (2003), no. 4, 441–478. MR 1997348, DOI 10.1090/S0273-0979-03-00991-1
J-P. Serre: Inaugural Minerva Lecture, “Equidistribution”, https:www.math.princeton.edu/ events/seminars/minerva-lectures/inaugural-minerva-lectures-i-equidistribution
Tamás Szamuely, Galois groups and fundamental groups, Cambridge Studies in Advanced Mathematics, vol. 117, Cambridge University Press, Cambridge, 2009. MR 2548205, DOI 10.1017/CBO9780511627064
H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1914).
References
- Pierre Deligne, La conjecture de Weil. II, Inst. Hautes Études Sci. Publ. Math. 52 (1980), 137–252 (French). MR 601520 (83c:14017)
- 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, DOI 10.1090/S0273-0979-2011-01335-0
- 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), DOI 10.1215/S0012-7094-96-08317-9
- Henryk Iwaniec, Topics in classical automorphic forms, Graduate Studies in Mathematics, vol. 17, American Mathematical Society, Providence, RI, 1997. MR 1474964 (98e:11051)
- 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)
- 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)
- 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), DOI 10.1090/S0273-0979-1990-15922-1
- Nicholas M. Katz, Exponential sums and differential equations, Annals of Mathematics Studies, vol. 124, Princeton University Press, Princeton, NJ, 1990. MR 1081536 (93a:14009)
- 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)
- 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)
- 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), DOI 10.4007/annals.2005.161.489
- 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), DOI 10.1088/0951-7715/20/10/001
- 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), DOI 10.1090/S0273-0979-2011-01359-3
- Barry Mazur, Finding meaning in error terms, Bull. Amer. Math. Soc. (N.S.) 45 (2008), no. 2, 185–228. MR 2383303 (2009c:11083), DOI 10.1090/S0273-0979-08-01207-X
- Peter Sarnak, Spectra of hyperbolic surfaces, Bull. Amer. Math. Soc. (N.S.) 40 (2003), no. 4, 441–478. MR 1997348 (2004f:11107), DOI 10.1090/S0273-0979-03-00991-1
- J-P. Serre: Inaugural Minerva Lecture, “Equidistribution”, https:www.math.princeton.edu/ events/seminars/minerva-lectures/inaugural-minerva-lectures-i-equidistribution
- Tamás Szamuely, Galois groups and fundamental groups, Cambridge Studies in Advanced Mathematics, vol. 117, Cambridge University Press, Cambridge, 2009. MR 2548205 (2011b:14064), DOI 10.1017/CBO9780511627064
- 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
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.
