Book Review
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MathSciNet review:
1567462
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Book Information:
Authors:
M. Scott Osborne and
Garth Warner
Title:
The theory of Eisenstein systems
Additional book information:
Academic Press, New York, 1981, xiii + 385 pp., $55.00. ISBN 0-1252-9250-3.
Werner O. Amrein, Josef M. Jauch, and Kalyan B. Sinha, Scattering theory in quantum mechanics, Lecture Notes and Supplements in Physics, No. 16, W. A. Benjamin, Inc., Reading, Mass.-London-Amsterdam, 1977. Physical principles and mathematical methods. MR 0495999
2. J. Arthur, A trace formula for reductive groups. I, Duke Math. J. 45 (1978), II, Compositio Math. 40 (1980).
James Arthur, The trace formula in invariant form, Ann. of Math. (2) 114 (1981), no. 1, 1–74. MR 625344, DOI 10.2307/1971376
James Arthur, On the inner product of truncated Eisenstein series, Duke Math. J. 49 (1982), no. 1, 35–70. MR 650368
James Arthur, On a family of distributions obtained from Eisenstein series. I. Application of the Paley-Wiener theorem, Amer. J. Math. 104 (1982), no. 6, 1243–1288. MR 681737, DOI 10.2307/2374061
James Arthur, A Paley-Wiener theorem for real reductive groups, Acta Math. 150 (1983), no. 1-2, 1–89. MR 697608, DOI 10.1007/BF02392967
Michel Duflo and Jean-Pierre Labesse, Sur la formule des traces de Selberg, Ann. Sci. École Norm. Sup. (4) 4 (1971), 193–284. MR 437462
8. M. Eichler, Lectures on modular correspondences, Tata Institute of Fundamental Research, Bombay, 1957.
Yuval Z. Flicker, The trace formula and base change for $\textrm {GL}(3)$, Lecture Notes in Mathematics, vol. 927, Springer-Verlag, Berlin-New York, 1982. MR 663002
I. M. Gel′fand and S. V. Fomin, Geodesic flows on manifolds of constant negative curvature, Uspehi Matem. Nauk (N.S.) 7 (1952), no. 1(47), 118–137 (Russian). MR 0052701
I. M. Gel′fand, Automorphic functions and the theory of representations, Proc. Internat. Congr. Mathematicians (Stockholm, 1962) Inst. Mittag-Leffler, Djursholm, 1963, pp. 74–85. MR 0175997
James Glimm and Arthur Jaffe, Quantum physics, Springer-Verlag, New York-Berlin, 1981. A functional integral point of view. MR 628000
13. R. Godement, Introduction aux travaux de Selberg, Sem. Bourbaki, 1957.
14. R. Godement, Fonctions holomorphes de carré sommable dans le demi-plan de Siegel, Sem. H. Cartan, 1957/58.
15. Harish-Chandra, Automorphic forms on semi-simple Lie groups, Lecture Notes in Math., vol. 62, Springer-Verlag, Berlin and New York, 1968.
Robert P. Langlands, On the functional equations satisfied by Eisenstein series, Lecture Notes in Mathematics, Vol. 544, Springer-Verlag, Berlin-New York, 1976. MR 0579181
Hans Maass, Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 121 (1949), 141–183 (German). MR 31519, DOI 10.1007/BF01329622
Walter Roelcke, Über die Wellengleichung bei Grenzkreisgruppen erster Art, S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl. 1953/1955 (1953/1955), 159–267 (1956) (German). MR 0081967
W. Roelcke, Analytische Fortsetzung der Eisensteinreihen zu den parabolischen Spitzen von Grenzkreisgruppen erster Art, Math. Ann. 132 (1956), 121–129 (German). MR 82562, DOI 10.1007/BF01452322
Walter Roelcke, Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene, I, Math. Ann. 167 (1966), no. 4, 292–337 (German). MR 1513277, DOI 10.1007/BF01364540
A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87. MR 88511
Atle Selberg, Discontinuous groups and harmonic analysis, Proc. Internat. Congr. Mathematicians (Stockholm, 1962) Inst. Mittag-Leffler, Djursholm, 1963, pp. 177–189. MR 0176097
- 1.
- W. O. Amrein, J. M. Jauch and K. B. Sinha, Scattering theory in quantum mechanics, Benjamin, New York, 1977. MR 0495999
- 2.
- J. Arthur, A trace formula for reductive groups. I, Duke Math. J. 45 (1978), II, Compositio Math. 40 (1980).
- 3.
- J. Arthur, The trace formula in invariant form, Ann. of Math. (2) 114 (1981). MR 625344
- 4.
- J. Arthur, On the inner product of truncated Eisenstein series, Duke Math. J. 49 (1982). MR 650368
- 5.
- J. Arthur, On a family of distributions obtained from Eisenstein series. I: Application of the Paley-Wiener theorem; II: Explicit formulas, Amer. J. Math., vol. 104 (1982). MR 681737
- 6.
- J. Arthur, A Paley-Wiener theorem for real reductive groups, Acta Math. (to appear). MR 697608
- 7.
- M. Duflo and J.-P. Labesse, Sur la formule des traces de Selberg, Ann. Sci. École Norm. Sup. (4) 4 (1971). MR 437462
- 8.
- M. Eichler, Lectures on modular correspondences, Tata Institute of Fundamental Research, Bombay, 1957.
- 9.
- Y. Flicker, The trace formula and base change for GL(3), Lecture Notes in Math., vol. 927, Springer-Verlag, Berlin and New York, 1982. MR 663002
- 10.
- I. M. Gelfand and S. V. Fomin, Geodesic flows on manifolds with constant negative curvature, Uspehi Math. Nauk 7 (1952). (Russian) MR 52701
- 11.
- I. M. Gelfand, Automorphic functions and the theory of representations, Proc. Internat. Congr. Math., Stockholm, 1962. MR 175997
- 12.
- J. Glimm and A. Jaffe, Quantum physics, Springer-Verlag, Berlin and New York, 1981. MR 628000
- 13.
- R. Godement, Introduction aux travaux de Selberg, Sem. Bourbaki, 1957.
- 14.
- R. Godement, Fonctions holomorphes de carré sommable dans le demi-plan de Siegel, Sem. H. Cartan, 1957/58.
- 15.
- Harish-Chandra, Automorphic forms on semi-simple Lie groups, Lecture Notes in Math., vol. 62, Springer-Verlag, Berlin and New York, 1968.
- 16.
- R. P. Langlands, On the functional equations satisfied by Eisenstein series, Lecture Notes in Math., vol. 544, Springer-Verlag, Berlin and New York, 1976. MR 579181
- 17.
- H. Maass, Über eine neue Art von nichtanalytischen automorphen Funktionen, Math. Ann. 121 (1949). MR 31519
- 18.
- W. Roelcke, Über die Wellengleichung bei Grenzkreisgruppen erster Art, Sitzungsber Heidelb. Akad. Wiss. Math.-Natur. Kl. 1953/1955 (1956), 159-267. MR 81967
- 19.
- W. Roelcke, Analytische Fortsetzung der Eisensteinreihen zu den parabolischen Spitzen von Grenzkreisgruppen erster Art, Math. Ann. 132 (1956), 121-129. MR 82562
- 20.
- W. Roelcke, Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I, Math. Ann. 167 (1966), II, Math. Ann. 168 (1967). MR 1513277
- 21.
- A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet Series, J. Indian Math. Soc. (N.S.) 20 (1956), 47-87. MR 88511
- 22.
- A. Selberg, Discontinuous groups and harmonic analysis, Proc. Internat. Congr. Math., Stockholm, 1962. MR 176097
Review Information:
Reviewer:
R. P. Langlands
Journal:
Bull. Amer. Math. Soc.
9 (1983), 351-361
DOI:
https://doi.org/10.1090/S0273-0979-1983-15206-0
