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Bulletin of the American Mathematical Society
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Book Information

Author(s): A. Borel
Title: Automorphic forms on $SL_{2}(\mathbf{R})$
Additional book information: Cambridge Tracts in Mathematics, vol. 130, Cambridge University Press, 1997, xiv+574 pp., $47.95, ISBN 0-521-58049-8

Author(s): D. Bump
Title: Automorphic forms and representations
Additional book information: Cambridge Studies in Advanced Mathematics, vol. 55, Cambridge University Press, 1997, xiv+574 pp., $79.95, ISBN 0-521-55098-X

Author(s): H. Iwaniec
Title: Topics in classical automorphic forms
Additional book information: Graduate Studies in Math., vol. 17, American Mathematical Society, Providence, RI, 1997, xii + 259, $39.00, ISBN 0-8218-0777-3


References:

[AR]
J. Adams and B. Roberts, Notes on the theta correspondence, Workshop at U. Maryland, 1994, www.math.umd.edu/~jda/preprints.

[A1]
J. Arthur, Stability and endoscopy: informal motivation, In: [BK]. CMP 98:03

[A2]
J. Arthur, Unipotent automorphic representations:conjectures, In: Orbites Unipotentes et Représentations II. Groupes p-adic et Réel, Astérisque 171-172 (1989), 13-71. MR 91f:22030

[A3]
J. Arthur, The problem of classifying automorphic representations of classical groups, CRM Proceedings and Lecture Notes, vol. 11, Amer. Math. Soc., Providence, RI, 1997. CMP 98:04

[A4]
J. Arthur, The Selberg trace formula for groups of F-rank one, Annals of Math. 100 (1974), 326-385. MR 50:12920

[AC]
J. Arthur and L. Clozel, Simple algebras, base change, and the advanced theory of the trace formula, Annals of Math. Studies 120, Princeton U. Press, 1989. MR 90m:22041

[BR]
D. Blasius and J. Rogawski, Zeta-functions of Shimura varieties, In: Motives (U. Jannsen and J.-P. Serre, eds.), Proc. Symp. Pure Math. 55, Part II, Amer. Math. Soc., Providence, 1994, 525-571. MR 95e:11051

[Bo]
A. Borel, Automorphic forms on SL$_{2}(\mathbf{R),}$ Cambridge Tracts in Math. 130, Cambridge U. Press, 1997. CMP 98:04

[BC]
A. Borel and W. Casselman (eds.), Automorphic forms, representations, and L-functions, Proc. Symp. Pure Math. 33, Parts I & II, Amer. Math. Soc., Providence, 1977. MR 80g:10002a; MR 80g:10002b

[BM]
A. Borel and G. Mostow (eds.), Algebraic groups and discontinuous subgroups, Proc. Symp. Pure Math. 9, Amer. Math. Soc., Providence, 1966. MR 34:2381

[BK]
T. N. Bailey and A. W. Knapp (eds.), Representation theory and automorphic forms, Proc. Symposia in Pure Math. 61, AMS, Providence 1997. CMP 98:03

[Bu]
D. Bump, Automorphic forms and representations, Cambridge Studies in Adv. Math. 55, Cambridge U. Press, 1997. MR 97k:11080

[BuK]
C. Bushnell and P. Kutzko, The admissible dual of $GL(N)$ via compact open subgroups, Annals of Math. Studies 129, Princeton U. Press, Princeton, NJ, 1993. MR 94h:22007

[CM]
L. Clozel and J. Milne (eds.), Automorphic forms, Shimura varieties, and L-functions, Perspectives in Math. 10 and 11, Academic Press, Boston, 1990. MR 90j:11002; MR 90j:11003

[De]
P. Deligne, Formes modulaires et représentations de $GL(2),$ In: Modular functions of one variable II, Springer Lecture Notes 349, Springer Verlag, Berlin, 1973. MR 52:10602

[DL]
M. Duflo and J.-P. Labesse, Sur la formule des traces de Selberg, Ann. Sci. École Norm. Sup. (4) 4 (1971), 193-284. MR 55:10392

[Du]
W. Duke, Some old problems and new results about quadratic forms, Notices of the AMS 44 (1997), 190-196 (www.ams.org/new-in-math/noticesfeatures). MR 97i:11035

[G1]
S. Gelbart, Automorphic forms on adele groups, Annals of Math. Studies 83, Princeton U. Press, 1975. MR 52:280

[G2]
S. Gelbart, An elementary introduction to the Langlands program, Bull. Amer. Math. Soc. 10 (1984), 177-219. MR 85e:11094

[G3]
S. Gelbart, The Arthur-Selberg trace formula, Univ. Lecture Series 9, American Math. Soc., Providence, RI, 1996. MR 98d:22017

[GJ]
S. Gelbart and H. Jacquet, Automorphic forms on $GL(2)$ $\emph{from}$ the analytic point of view, In [BC], Part I, 213-251. MR 81e:10024

[GS]
S. Gelbart and F. Shahidi, Analytic properties of automorphic L-functions, Academic Press, Boston (1988). MR 89f:11077

[GGPS]
I. Gelfand, M. Graev, I. Piatetski-Shapiro, Representation theory and automorphic forms, Saunders, Philadelphia, 1969. MR 38:2093

[He]
D. Hejhal, The Selberg Trace Formula for PSL$_{2}(\mathbf{R)},$ Springer Lecture Notes 548, Springer Verlag, Berlin, 1976. MR 55:12641

[Hi]
H. Hida, Elementary theory of L-functions and Eisenstein series, Cambridge University Press, 1993. MR 94j:11044

[Ho]
R. Howe, Theta series and invariant theory, In: [BC], Part I, 275-286. MR 81f:22034

[I1]
H. Iwaniec, Topics in Classical Automorphic Forms, Graduate Studies in Math. 17, Amer. Math. Soc., Providence, 1997. MR 98e:11051

[I2]
H. Iwaniec, Introduction to the Spectral Theory of Automorphic Forms, Rev. Mat. Iberoamericana, Madrid, 1995. MR 96f:11078

[I3]
H. Iwaniec, Fourier coefficients of modular forms of half-integral weight, Invent. Math 87 (1987), 385-401. MR 88b:11024

[J1]
H. Jacquet, Note on the analytic continuation of Eisenstein series, In [BK], 443-455. CMP 98:03

[J2]
H. Jacquet, Principal L-functions for $\mathrm{GL}(n)$, In [BK], 321-329. CMP 98:03

[JL]
H. Jacquet and R. P. Langlands, Automorphic forms on GL(2), Springer Lecture Notes 114, Springer Verlag, Berlin, 1970. MR 53:5481

[JS]
H. Jacquet and J. Shalika, On Euler products and the classification of automorphic representations, I and II, Amer. J. Math. 103 (1981), 499-588 and 777-815. MR 82m:10050a; MR 82m:10050b

[K1]
A. Knapp, Introduction to the Langlands Program, In [BK], 245-302. CMP 98:03

[K2]
A. Knapp, Theoretical aspects of the trace formula for GL(2), In [BK], 355-405. CMP 98:03

[Ko]
R. Kottwitz, Stable trace formula: elliptic singular terms, Math. Annalen 275 (1986), 365-399. MR 88d:22027

[Ku]
S. Kudla, The local Langlands correspondence, the non-archimedean case. In: Motives (U. Jannsen and J.-P. Serre, eds.), Proc. Symp. Pure Math. 55, Part II, Amer. Math. Soc., Providence, RI, 1994, 365-391. MR 95d:11065

[L1]
R. Langlands, Problems in the theory of automorphic forms, In: Lectures in Modern Analysis, Springer Lecture Notes 170 (1970), 18-61. MR 46:1758

[L2]
R. Langlands, Base change for $GL(2),$ Annals of Math. Studies 96, Princeton U. Press, 1980. MR 82a:10032

[L3]
R. Langlands, Where stands functoriality today?, In [BK], 457-471. CMP 98:03

[L4]
R. Langlands, Representation theory, its rise and role in number theory, In: Proc. Gibbs Symposium, Amer. Math. Soc., Providence, RI, 1990, 181-210. MR 92d:11053

[LR]
R. Langlands and D. Ramakrishnan (eds.) , The Zeta-functions of Picard Modular Surfaces, CRM Pubs., Montreal, 1992. MR 92m:14001

[LS]
R. Langlands and D. Shelstad, On the definition of transfer factors, Math. Annalen 278 (1987), 219-271. MR 89c:11172

[La]
G. Laumon, Cohomology of Drinfeld modular varieties, I and II, Cambridge Studies in Adv. Math., Cambridge U. Press, 1995. MR 98c:11045a; MR 98c:11045b

[LRS]
W. Luo, Z. Rudnick, and P. Sarnak, On Selberg's eigenvalue conjecture, Geom. Funct. Anal. 5 (2) (1995), 387-401. MR 96h:11045

[MW]
C. Moeglin and J.-L. Waldspurger, Spectral decomposition and Eisenstein series, Cambridge Tracts in Math. 113, Cambridge U. Press, 1995. MR 97d:11083

[Mo]
C. Moeglin, Representations of $\emph{GL(n,F)}$ in the non-archimedean case, In [BK], 303-319. CMP 98:03

[Pr]
D. Prasad, A brief survey of the theta correspondence, Contemporary Math. 210, Amer. Math. Soc. (1998), 171-193. CMP 98:03

[Ra]
D. Ramakrishnan, Regulators, algebraic cycles, and values of L-functions, In: Contemporary Math. 83, Amer. Math. Soc. (1989), 189-310. MR 90e:11094

[Ri]
K. Ribet, A modular construction of unramified p-extensions of $\mathbf{Q}(\mu _{p}),$ Invent. Math. 34 (3) (1976), 151-162. MR 54:7424

[Ro]
J. Rogawski, Functoriality and the Artin conjecture. In [BK], 331-353. CMP 98:03

[S1]
P. Sarnak, Some applications of modular forms, Cambridge Tracts in Mathematics 99, Cambridge U. Press (1990). MR 92k:11045

[S2]
P. Sarnak, On cusp forms, In: The Selberg trace formula and related topics, Contemp. Math. 53, Amer. Math. Soc., Providence, 1986. MR 87j:11047

[S3]
P. Sarnak, Selberg's eigenvalue conjecture, Notices Amer. Math. Soc. 42 (1995), 1272-1277. MR 97c:11059

[Sel]
A. Selberg, Harmonic Analysis, In Collected Papers I, Springer Verlag, Berlin, 1989. MR 92h:01083

[Ser]
J.-P. Serre, A Course in Arithmetic, Graduate Texts in Math. 7, Springer Verlag, Berlin, 1973. MR 49:8956

[Sh]
G. Shimura, Introduction to the Arithmetic theory of Automorphic Forms, Pub. Math. Soc. Japan 11, I. Shoten and Princeton U. Press, 1971. MR 95e:11048

[Wa]
J.-L. Waldspurger, Répresentations métaplectiques et conjectures de Howe, Séminaire Bourbaki 1986/87, Asterisque 152-153 (3) (1987), 85-99. MR 89g:11039

[W1]
A. Weil, Sur certaines groupes d'opérateurs unitaires, Acta Math. 111 (1964), 143-211. MR 29:2324

[W2]
A. Weil, Elliptic functions according to Eisenstein and Kronecker, Ergebnisse der Mathematik und ihrer Grenzgebiete 88, Springer Verlag, Berlin, 1976. MR 58:27769a


Additional Information:

Reviewer(s):
Jonathan D. Rogawski
Affiliation: University of California, Los Angeles
Email: jonr@math.ucla.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 35 (1998), 253-263.

MSC (1991): Primary 11F12, 11F70, 11F72, 11F66, 11F11, 11F27; Secondary 22E46, 11R39, 11E25
DOI: 10.1090/S0273-0979-98-00756-3
PII: S 0273-0979(98)00756-3
Copyright of article: Copyright 1998, American Mathematical Society


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