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Book Review

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Book Information:

Author: Roelof W. Bruggeman
Title: Families of automorphic forms
Additional book information: Monographs Math., vol. 88, Birkhäuser, Basel and Boston, MA, 1994, x + 317 pp., ISBN 3-7643-5046-6, $99.00$

E. T. Bell, Men of mathematics, Simon and Schuster, NY, 1937.

Yves Colin de Verdière, Pseudo-laplaciens. II, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 2, 87–113 (French). MR 699488

P. Garrett, Review of Harmonic analysis on symmetric spaces and applications, Vols. I, II, Bull. Amer. Math. Soc. (N.S.) 22 (1990), 219--229.

D. Grenier, Factoring L-functions as products of L-functions, Trans. Amer. Math. Soc. 345 (1994), 673--692. CMP 94:16

Martin C. Gutzwiller, Chaos in classical and quantum mechanics, Interdisciplinary Applied Mathematics, vol. 1, Springer-Verlag, New York, 1990. MR 1077246, DOI 10.1007/978-1-4612-0983-6

Dennis A. Hejhal, A continuity method for spectral theory on Fuchsian groups, Modular forms (Durham, 1983) Ellis Horwood Ser. Math. Appl.: Statist. Oper. Res., Horwood, Chichester, 1984, pp. 107–140. MR 803365

Dennis A. Hejhal and Barry N. Rackner, On the topography of Maass waveforms for $\textrm {PSL}(2,\textbf {Z})$, Experiment. Math. 1 (1992), no. 4, 275–305. MR 1257286

Shôkichi Iyanaga and Yukiyosi Kawada (eds.), Encyclopedic dictionary of mathematics, Translated from the second Japanese edition, MIT Press, Cambridge, Mass.-London, 1980. Translation reviewed by Kenneth O. May; With a foreword by Saunders Mac Lane. MR 591028

Svetlana Katok, Fuchsian groups, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1992. MR 1177168

Serge Lang, Introduction to modular forms, Grundlehren der Mathematischen Wissenschaften, No. 222, Springer-Verlag, Berlin-New York, 1976. MR 0429740

R. P. Langlands, Review of The theory of Eisenstein systems, Bull. Amer. Math. Soc. (N.S.) 9 (1983), 351--361.

A. Lubotzky, Discrete groups, expanding graphs, and invariant measures, Birkhäuser, Basel and Boston, MA, 1994. CMP 95:05

H. Maass, Lectures on modular functions of one complex variable, 2nd ed., Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 29, Tata Institute of Fundamental Research, Bombay, 1983. With notes by Sunder Lal. MR 734485, DOI 10.1007/978-3-662-02380-8

R. S. Phillips and P. Sarnak, The Weyl theorem and the deformation of discrete groups, Comm. Pure Appl. Math. 38 (1985), no. 6, 853–866. MR 812352, DOI 10.1002/cpa.3160380614

P. Sarnak, Arithmetic quantum chaos, The Schur Lectures (I. Piatetski-Shapiro and S. Gelbart, eds.), Israel Math. Conf. Proc., Vol. 8, Bar-Ilan University, Israel, 1995, pp. 183--236.

Peter Sarnak, Some applications of modular forms, Cambridge Tracts in Mathematics, vol. 99, Cambridge University Press, Cambridge, 1990. MR 1102679, DOI 10.1017/CBO9780511895593

Atle Selberg, Collected papers. Vol. I, Springer-Verlag, Berlin, 1989. With a foreword by K. Chandrasekharan. MR 1117906

Audrey Terras, Harmonic analysis on symmetric spaces and applications. I, Springer-Verlag, New York, 1985. MR 791406, DOI 10.1007/978-1-4612-5128-6

------, Review of Introduction to modular forms, Bull. Amer. Math. Soc. (N.S.) 2 (1980), 206--214.

D. I. Wallace, The Selberg trace formula for $\textrm {SL}(3,\textbf {Z})\backslash \textrm {SL}(3,\textbf {R})/\textrm {SO}(3,\textbf {R})$, Trans. Amer. Math. Soc. 345 (1994), no. 1, 1–36. MR 1184117, DOI 10.1090/S0002-9947-1994-1184117-4

Hans Rademacher and Emil Grosswald, Dedekind sums, The Carus Mathematical Monographs, No. 16, Mathematical Association of America, Washington, D.C., 1972. MR 0357299

Review Information:

Reviewer: Audrey A. Terras
Affiliation: University of California San Diego
Email: aterras@ucsd.edu