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Book Information:
Author:
C. Moeglin and J.-L. Waldspurger
Title:
Spectral decomposition and Eisenstein series
Additional book information:
Cambridge Univ. Press,
Cambridge, New York, and Melbourne,
1995,
xxvii+ 335 pp.,
ISBN 0-521-41893-3,
$80.00$
James G. Arthur, A trace formula for reductive groups. I. Terms associated to classes in $G(\textbf {Q})$, Duke Math. J. 45 (1978), no. 4, 911–952. MR 518111
James Arthur, Eisenstein series and the trace formula, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 253–274. MR 546601
James Arthur, Unipotent automorphic representations: global motivation, Automorphic forms, Shimura varieties, and $L$-functions, Vol. I (Ann Arbor, MI, 1988) Perspect. Math., vol. 10, Academic Press, Boston, MA, 1990, pp. 1–75. MR 1044818
4. E. P. van den Ban and H. Schlichtkrull, `A residue calculus for root systems', preprint, 1997.
Yves Colin de Verdière, Une nouvelle démonstration du prolongement méromorphe des séries d’Eisenstein, C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), no. 7, 361–363 (French, with English summary). MR 639175
Isaac Y. Efrat, The Selberg trace formula for $\textrm {PSL}_2(\textbf {R})^n$, Mem. Amer. Math. Soc. 65 (1987), no. 359, iv+111. MR 874084, DOI 10.1090/memo/0359
7. Jens Franke, `Harmonic analysis in weighted 
-spaces', Ann. Sci. École Norm. Sup. 31 (1998), 181-279. CMP 98:08
R. Godement, The decomposition of $L^{2}\,(G/\Gamma )$ for $\Gamma =\textrm {SL}(2,\,Z)$, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 211–224. MR 0210827
9. R. Godement, `Introduction á la théorie de Langlands', Sém. Bourbaki 321 (1967/68).
G. Harder, Chevalley groups over function fields and automorphic forms, Ann. of Math. (2) 100 (1974), 249–306. MR 563090, DOI 10.2307/1971073
Harish-Chandra, Automorphic forms on semisimple Lie groups, Lecture Notes in Mathematics, No. 62, Springer-Verlag, Berlin-New York, 1968. Notes by J. G. M. Mars. MR 0232893
Tomio Kubota, Elementary theory of Eisenstein series, Kodansha, Ltd., Tokyo; Halsted Press [John Wiley & Sons, Inc.], New York-London-Sydney, 1973. MR 0429749
R. P. Langlands, Eisenstein series, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 235–252. MR 0249539
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
Morgan Ward and R. P. Dilworth, The lattice theory of ova, Ann. of Math. (2) 40 (1939), 600–608. MR 11, DOI 10.2307/1968944
C. Mœglin and J.-L. Waldspurger, Le spectre résiduel de $\textrm {GL}(n)$, Ann. Sci. École Norm. Sup. (4) 22 (1989), no. 4, 605–674 (French). MR 1026752
L. E. Morris, Eisenstein series for reductive groups over global function fields. I. The cusp form case, Canadian J. Math. 34 (1982), no. 1, 91–168. MR 650855, DOI 10.4153/CJM-1982-009-2
L. E. Morris, Eisenstein series for reductive groups over global function fields. I. The cusp form case, Canadian J. Math. 34 (1982), no. 1, 91–168. MR 650855, DOI 10.4153/CJM-1982-009-2
Werner Müller, The trace class conjecture in the theory of automorphic forms, Ann. of Math. (2) 130 (1989), no. 3, 473–529. MR 1025165, DOI 10.2307/1971453
20. W. Müller, `On the analytic continuation of rank one Eisenstein series', Geom. Funct. Anal. 6 (1996), pp. 572-586. CMP 96:13
21. M. S. Osborne and G. Warner, The theory of Eisenstein systems, Pure and Appl. Math. 99, Academic Press, 1981.
M. Scott Osborne and Garth Warner, The Selberg trace formula. II. Partition, reduction, truncation, Pacific J. Math. 106 (1983), no. 2, 307–496. MR 699915
Cahit Arf, Untersuchungen über reinverzweigte Erweiterungen diskret bewerteter perfekter Körper, J. Reine Angew. Math. 181 (1939), 1–44 (German). MR 18, DOI 10.1515/crll.1940.181.1
- 1.
- J. Arthur, `A trace formula for reductive groups I: terms associated to classes in
', Duke Math. Jour. 45 (1978), pp. 911-951. MR 0518111
- 2.
- J. Arthur, `Eisenstein series and the trace formula', in Automorphic Forms, Representations, and
-functions, Proc. Symp. Pure Math. XXXIII, eds. A. Borel and W. Casselman,
A. M. S., 1979, pp. 253-274. MR 0546601
- 3.
- J. Arthur, `Unipotent automorphic representations: global motivations', in Automorphic forms, Shimura varieties, and -functions II, Academic Press, 1990. MR 1044818
- 4.
- E. P. van den Ban and H. Schlichtkrull, `A residue calculus for root systems', preprint, 1997.
- 5.
- Y. Colin de Verdière, `Une nouvelles démonstration du prolongement méromorphe des séries d'Eisenstein', C. R. A. S. 293 (1981), pp. 361-363. MR 0639175
- 6.
- I. Y. Efrat, The Selberg trace formula for
, Memoirs of the A. M. S. 65, no. 359, 1987. MR 0874084
- 7.
- Jens Franke, `Harmonic analysis in weighted -spaces', Ann. Sci. École Norm. Sup. 31 (1998), 181-279. CMP 98:08
- 8.
- R. Godement, `The decomposition of
', in Algebraic groups and discontinuous subgroups, Proc. Symp. Pure Math. IX, A. M. S., 1966. MR 0210827
- 9.
- R. Godement, `Introduction á la théorie de Langlands', Sém. Bourbaki 321 (1967/68).
- 10.
- G. Harder, `Chevalley groups over function fields and automorphic forms', Ann. Math. 100 (1974), pp. 249-306. MR 0563090
- 11.
- Harish-Chandra, Automorphic forms on semi-simple Lie groups, Lect. Notes Math. 62, Springer, 1968. MR 0232893
- 12.
- T. Kubota, Elementary Theory of Eisenstein Series, Kodansha and J. Wiley, 1973. MR 0429749
- 13.
- R. P. Langlands, `Eisenstein series', in Algebraic groups and discontinuous subgroups, Proc. Symp. Pure Math. IX, A. M. S., 1966. MR 0249539
- 14.
- R. P. Langlands, On the functional equations satisfied by Eisenstein series, Lect. Notes Math. 544, Springer, 1976. MR 0579181
- 15.
- H. Maass, `Über eine neue Art von nichtanalytischen automorphen Funktionedn und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen', Mat. Ann. 121 (1949), pp. 141-183. MR 11:163c
- 16.
- C. Moeglin and J.-L. Waldspurger, `Le spectre résiduel de
', Ann. Sci. Éc. Norm. Sup. 22 (1989), pp. 605-674. MR 1026752
- 17.
- L. Morris, `Eisenstein series for reductive groups over global function fields I: the cusp form case', Can. Jour. Math. 34 (1982), pp. 91-168. MR 0650855
- 18.
- L. Morris, `Eisenstein series for reductive groups over global function fields II: the general case', Can. Jour. Math. 34 (1982), pp. 1112-82. MR 0650855
- 19.
- W. Müller, `The trace class conjecture in the theory of automorphic forms', Ann. Math. 130 (1989), pp. 473-530. MR 1025165
- 20.
- W. Müller, `On the analytic continuation of rank one Eisenstein series', Geom. Funct. Anal. 6 (1996), pp. 572-586. CMP 96:13
- 21.
- M. S. Osborne and G. Warner, The theory of Eisenstein systems, Pure and Appl. Math. 99, Academic Press, 1981.
- 22.
- M. S. Osborne and G. Warner, `Partition, reduction, truncation', Pac. Jour. Math. 106 (1983), pp. 307-496. MR 0699915
- 23.
- W. Roelcke, `Analytische Fortsetzung der Eisensteinreihen zu den parabolischen Spitzen von Grenzkreisgruppen erster Art', Math. Ann. 132 (1956), pp. 121-129. MR 18:571b
Review Information:
Reviewer:
Bill Casselman
Affiliation:
University of British Columbia
Email:
cass@math.ubc.ca
Journal:
Bull. Amer. Math. Soc.
35 (1998), 243-247
DOI:
https://doi.org/10.1090/S0273-0979-98-00752-6
Review copyright:
© Copyright 1998
American Mathematical Society
