# The collected works of James G. Arthur

## The papers (arranged by year of publication)

[1]**The Selberg trace formula for groups of F-rank one**, *Annals of Mathematics (2)* **100** (1974), 326–385.

[**MR0360470**: reviewed by J.-P. Labesse]

[2]**Some tempered distributions on semisimple groups of real rank one**, *Annals of Mathematics (2)* **100** (1974), 553–584.

[**MR0360934**: reviewed by P. C. Trombi]

[3]**Harmonic analysis of the Schwartz space of a reductive Lie group I,II**, preprint, 1974.

[4]**A theorem on the Schwartz space of a reductive Lie group**, *Proceedings of the National Academy of Sciences U.S.A.* **72** (1975), 4718–4719.

[**MR0460539**: reviewed by P. C. Trombi]

[5]**The characters of discrete series as orbital integrals**, *Inventiones Mathematicae* **32** (1976), 205–261.

[**MR0412348**: reviewed by E. A. Thieleker]

[6]**A truncation process for reductive groups**, *Bulletin of the American Mathematical Society* **83** (1977), 748–750.

[**MR0480886**]

[7]**Eisenstein series and the trace formula**, pages 253–274 in **Automorphic forms, representations and L-functions**, *Proceedings of Symposia in Pure Mathematics* **33, Part 1**, American Mathematical Society, Providence, RI, 1979.

[**MR0546601**: reviewed by A. B. Venkov]

[8]**A trace formula for reductive groups I. Terms associated to classes in G(Q)**, *Duke Mathematics Journal* **45** (1978), 911–952.

[**MR0518111**: reviewed by Stephen Gelbart]

[9]**Harmonic analysis of invariant distributions**, pages 384–393 in **Lie theories and their applications**, *Queen's Papers in Pure and Applied Mathematics* **48**, Queen's University, Kingston, Ontario, 1978.

[**MR0500463**: reviewed by P. C. Trombi]

[10]**A trace formula for reductive groups II. Applications of a truncation operator**, *Compositio Mathematicae* **40** (1980), 87–121.

[**MR0558260**: reviewed by Stephen Gelbart]

[11]**The trace formula in invariant form**, *Annals of Mathematics (2)* **114** (1981), 1–74.

[**MR0625344**: reviewed by Freydoon Shahidi]

[12]**Automorphic representations and number theory**, pages 3–51 in **1980 Seminar on Harmonic Analysis (Montreal, Que., 1980)**, *CMS Conference Proceedings* **1**, American Mathematical Society, Providence, R.I., 1981.

[**MR0670091**: reviewed by Ernst-Wilhelm Zink]

[13]**On the inner product of truncated Eisenstein series**, *Duke Mathematics Journal* **49** (1982), 35–70.

[**MR0650368**: reviewed by Martin L. Karel]

[14]**On a family of distributions obtained from Eisenstein series I. Application of the Paley-Wiener theorem**, *American Journal of Mathematics* **104** (1982), 1243–1288.

[**MR0681737**]

[15]**On a family of distributions obtained from Eisenstein series II. Explicit formulas**, *American Journal of Mathematics* **104** (1982), 1289–1336.

[**MR0681738**: reviewed by Freydoon Shahidi]

[16]**A Paley-Wiener theorem for real reductive groups**, *Acta Mathematica* **150** (1983), 1–89.

[**MR0697608**: reviewed by P. C. Trombi]

[17]**The trace formula for reductive groups**, pages 1–41 in **Conference on automorphic theory**, *Publications Mathématiques Université Paris VII* **15**, Université Paris VII, Paris, 1983.

[**MR0723181**: reviewed by Stephen Gelbart]

[18]**Multipliers and a Paley-Wiener theorem for real reductive groups**, pages 1–19 in **Representation theory of reductive groups**, 1983.

[**MR0733803**: reviewed by D. Milicic]

[19]**On some problems suggested by the trace formula**, pages 1–49 in **Lie group representations, II**, *Lecture Notes in Mathematics* **1041**, Springer, Berlin, 1984.

[**MR0748504**: reviewed by A. B. Venkov]

[20]**The trace formula for noncompact quotient**, pages 849–859 in **Proceedings of the International Congress of Mathematicians**, 1984.

[**MR0804739**: reviewed by A. B. Venkov]

[21]**A measure on the unipotent variety**, *Canadian Journal of Mathematics* **37** (1985), 1237–1274.

[**MR0828844**: reviewed by A. B. Venkov]

[22]**On a family of distributions obtained from orbits**, *Canadian Journal of Mathematics* **38** (1986), 179–214.

[**MR0835041**: reviewed by A. B. Venkov]

[23]**The Fourier transform of weighted orbital integrals on SL(2,R)** (with Rebecca A. Herb and Paul J. Sally, Jr.), pages 17–37 in **The Selberg trace formula and related topics**, *Contemporary Mathematics* **53**, American Mathematical Society, Providence, RI, 1986.

[**MR0853551**: reviewed by Stephen Gelbart]

[24]**The characters of supercuspidal representations as weighted orbital integrals**, *Proceedings of the Indian Academy of Sciences: Mathematical Sciences* **97** (1987), 3–19.

[**MR0983600**: reviewed by David Manderscheid]

[25]**The local behaviour of weighted orbital integrals**, *Duke Mathematics Journal* **56** (1988), 223–293.

[**MR0932848**: reviewed by Stephen Gelbart]

[26]**Characters, harmonic analysis, and an L ^{2}-Lefschetz formula**, pages 167–179 in

**The mathematical heritage of Hermann Weyl**,

*Proceedings of Symposia in Pure Mathematics*

**48**, American Mathematical Society, Providence, RI, 1988.

[

**MR0974334**: reviewed by Roberto J. Miatello]

[27]**The invariant trace formula I. Local theory**, *Journal of the American Mathematical Society* **1** (1988), 323–383.

[**MR0928262**: reviewed by A. B. Venkov]

[28]**The invariant trace formula II. Global theory**, *Journal of the American Mathematical Society* **1** (1988), 501–554.

[**MR0939691**: reviewed by A. B. Venkov]

[29]**Intertwining operators and residues I. Weighted characters**, *Journal of Functional Analysis* **84** (1989), 19–84.

[**MR0999488**: reviewed by David Joyner]

[30]**Intertwining operators and residues II. Invariant distributions**, *Compositio Mathematicae* **70** (1989), 51–99.

[**MR0993173**: reviewed by David Joyner]

[31]**Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula** (with Laurent Clozel), **Princeton University Press, Princeton, NJ**, 1989.

[**MR1007299**: reviewed by Stephen Gelbart]

[32]**The trace formula and Hecke operators**, pages 11–27 in **Number theory, trace formulas and discrete groups**, 1989.

[**MR0993309**: reviewed by Werner Hoffmann]

[33]**The L^{2}-Lefschetz numbers of Hecke operators**,

*Inventiones Mathematicae*

**97**(1989), 257–290.

[

**MR1001841**: reviewed by Stephen Gelbart]

[34]**Harmonic analysis of tempered distributions on semisimple Lie groups of real rank one**, pages 13–100 in **Representation theory and harmonic analysis on semisimple Lie groups**, *Mathematical Surveys Monographs* **31**, American Mathematical Society, Providence, RI, 1989.

[Dissertation, Yale University, New Haven, CT, 1970]

[**MR1011896**: reviewed by Takeshi Kawazoe]

[35]**Unipotent automorphic representations: conjectures**, pages 13–71 in **Orbites unipotentes et représentations, II.**, *Astérisque* **171-172**, 1989.

[**MR1021499**: reviewed by Marko Tadić]

[36]**Unipotent automorphic representations: global motivation**, pages 1–75 in **Automorphic forms, Shimura varieties, and L-functions, Vol. I**, *Perspectives in Mathematics* **10**, Academic Press, Boston, MA, 1990.

[**MR1044818**: reviewed by Stephen Gelbart]

[37]**Towards a local trace formula**, pages 1–23 in **Algebraic analysis, geometry, and number theory**, 1989.

[**MR1463695**: reviewed by Werner Hoffmann]

[38]**Lectures on automorphic L-functions** (with Stephen Gelbart), pages 1–59 in **L-functions and arithmetic**, *London Math. Soc. Lecture Note Ser.* **153**, Cambridge Univ. Press, Cambridge, 1991.

[**MR1110389**: reviewed by David Manderscheid]

[39]**Some problems in local harmonic analysis**, pages 57–78 in **Harmonic analysis on reductive groups**, *Progress in Mathematics* **101**, Birkhäuser Boston MA, 1991.

[**MR1168477**: reviewed by Jeffrey Adams]

[40]**A local trace formula**, *Institut des Hautes Études Scientifiques Publications Mathématiques* **73** (1991), 5–96.

[**MR1114210**: reviewed by Stephen Gelbart]

[41]**On elliptic tempered characters**, *Acta Mathematica* **171** (1993), 73–138.

[**MR1237898**: reviewed by Rebecca Herb]

[42]**On the Fourier transforms of weighted orbital integrals**, *Journal für die Reine und Angewandte Mathematik* **452** (1994), 163–217.

[**MR1282200**: reviewed by Stephen Gelbart]

[43]**The trace Paley Wiener theorem for Schwartz functions**, pages 171–180 in **Representation theory and analysis on homogeneous spaces**, *Contemporary Mathematics* **177**, American Mathematical Society, Providence, RI, 1994.

[**MR1303605**: reviewed by Marko Tadić]

[44]**L ^{2}-cohomology and automorphic representations**, pages 1–17 in

**Canadian Mathematical Society 1945–1995, volume 3**, Canadian Mathematical Society, Ottawa, Ontario, 1996.

[

**MR1661609**: reviewed by Takeshi Kawazoe]

[45]**On local character relations**, *Selecta Math. (N.S.)* **2** (1996), 501–579.

[**MR1443184**]

[46]**The problem of classifying automorphic representations of classical groups**, pages 1–12 in **Advances in mathematical sciences: CRM's 25 years**, *None* **11**, 1997.

[**MR1479667**]

[47]**Stability and endoscopy: informal motivation**, pages 433–442 in **Representation theory and automorphic forms**, *Proceedings of Symposia in Pure Mathematics* **61**, American Mathematical Society, Providence, RI, 1997.

[**MR1476508**: reviewed by Dihua Jiang]

[48]**Canonical normalization of weighted characters and a transfer conjecture**, *Comptes Rendues Math. Acad. Sci. Soc. R. Can.* **20** (1998), 33–52.

[**MR1623485**: reviewed by Dihua Jiang]

[49]**Towards a stable trace formula**, pages 507–517 in **Proceedings of the International Congress of Mathematicians, Vol. II**, 1998.

[**MR1648100**: reviewed by Wee Teck Gan]

[50]**On the transfer of distributions: weighted orbital integrals**, *Duke Mathematics Journal* **99** (1999), 209–283.

[**MR1708030**: reviewed by Volker Heiermann]

[51]**Endoscopic L-functions and a combinatorial identity**, *Canadian Journal of Mathematics* **51** (1999), 1135–1148.

[Dedicated to H. S. M. Coxeter on the occasion of his 90th birthday]

[**MR1756875**: reviewed by Anton Deitmar]

[52]**Stabilization of a family of differential equations**, pages 77–95 in **The mathematical legacy of Harish-Chandra**, *Proceedings of Symposia in Pure Mathematics* **68**, American Mathematical Society, Providence, RI, 2000.

[**MR1767893**: reviewed by Anton Deitmar]

[53]**Harmonic analysis and group representations**, *Notices of the American Mathematical Society* **47** (2000), 26–34.

[**MR1733064**]

[54]**A stable trace formula II. Global descent**, *Inventiones Mathematicae* **143** (2001), 157–220.

[**MR1802795**: reviewed by Volker Heiermann]

[55]**A stable trace formula I. General expansions**, *Journal of the Institute of Mathematics of Jussieu* **1** (2002), 175–277.

[**MR1954821**: reviewed by Volker Heiermann]

[56]**A stable trace formula III. Proof of the main theorems**, *Annals of Mathematics (2)* **158** (2003), 769–873.

[**MR2031854**: reviewed by Volker Heiermann]

[57]**A note on the automorphic Langlands group**, *Canadian Mathematics Bulletin* **45** (2002), 466–482.

[Dedicated to Robert V. Moody]

[**MR1941222**: reviewed by Mahdi Asgari]

[58]**The principle of functoriality**, *Bulletin of the American Mathematical Society* **40** (2003), 39–53.

[A special issue on mathematical challenges of the 21st century, based on a conference in Los Angeles CA, 2000]

[**MR1943132**: reviewed by Mahdi Asgari]

[59]**Automorphic representations of GSp(4)**, pages 65–81 in **Contributions to automorphic forms, geometry, and number theory**, 2004.

[Conference in honor of Joe Shalika]

[**MR2058604**: reviewed by Jeff Hakim]

[60]**Armand Borel (1923–2003)** (with Enrico Bombieri, Komaravolu Chandrasekharan, Gopal Prasad, Jean-Pierre Serre, Tonny Springer, and Jacques Tits), *Notices of the American Mathematical Society* **51** (2004), 498–524.

[Reprinted in the *Asian Journal of Mathematics* **8** (2004), xlvii–xcvi]

[**MR2046057**: reviewed by Henry Heatherly]

[61]**Harmonic analysis in mathematics**, *Ideas* **2** (2005), 64.

[Published by the Faculty of Arts and Sciences, University of Toronto]

[62]**AMS President's address at Abel celebration**, *Notices Amer. Math. Soc.* **52** (2005), 745–746.

[**MR2159687**]

[63]**An introduction to the Trace Formula**, pages 1–263 in **Harmonic analysis, the trace formula, and Shimura varieties**, *Clay Mathematics Proceedings* **4**, American Mathematical Society, Providence, RI, 2005.

[**MR2192011**: reviewed by Erez Lapid]

[64]**A note on L-packets**, *Pure and Applied Mathematics Quarterly* **2** (2006), 199–217.

[**MR2217572**: reviewed by B. Sury]

[65]**An asymptotic formula for real groups**, *Journal für die Reine und Angewandte Mathematik* **601** (2006), 163–230.

[**MR2289209**: reviewed by David A. Renard]

[66]**Parabolic transfer for real groups**, *Journal of the American Mathematical Society* **21** (2008), 171–234.

[**MR2350054**: reviewed by David A. Renard]

[67]**A (very brief) history of the trace formula**, *Newsletter of the Pacific Institute for the Mathematical Sciences* **10** (2007), 8–11.

[68]**Problems for real groups**, pages 39–62 in **Representation theory of real reductive groups**, *Contemporary Mathematics* **472**, 2008.

[**MR2478455**: reviewed by Werner Hoffmann]

[69]**Report on the trace formula**, pages 1–12 in **Automorphic forms and L-functions I. Global aspects**, *Contemporary Mathematics* **488**, 2009.

[**MR2522025**: reviewed by Werner Hoffmann]

[70]**Induced representations, intertwining operators, and transfer for real groups**, pages 51–67 in **Group representations, ergodic theory, and mathematical physics: a tribute to George Mackey**, *Contemporary Mathematics* **449**, 2008.

[**MR2391798**: reviewed by David A. Renard]

[71]**The embedded eigenvalue problem for classical groups**, pages 19–31 in **On certain L-functions**, *Clay Mathematics Proceedings* **13**, American Mathematical Society, 2011.

[**MR2767508**: reviewed by Neven Grbac]

[72]**Transfer, the Fundamental Lemma, and the work of Waldspurger**, pages 7–9 in **Clay Mathematics Annual Report**, Clay Mathematics Institute, Cambridge, MA, 2009.

[73]**The work of Ngô Bau Châu**, pages 57–70 in **Proceedings of the International Congress of Mathematicians**, 2010.

[**MR2827882**]

[74]**The Endoscopic Classification of Representations: Orthogonal and Symplectic Groups. Published in 2013 as volume 61 in the series of Colloquium Publications by
the American Mathematical Society.**

[

**MR3135650**: reviewed by Dihua Jiang]

[75]**The endoscopic classification of representations**,
pages 1–22 in **Automorphic Representations and L-functions**, Tata Institute of Fundamental Research, 2013.

[**MR3156849**: reviewed by Zhengyu Mao]

[76]** Classifying automorphic representations**,
pages 1–58 in **Current Developments in Mathematics, Volume 2012**, International Press of Boston, 2013.

[**MR3204343**: reviewed by Ivan Matic]

[77]** L-functions and automorphic representations**, pages 171–197 in

**Proceedings of the International Congress of Matematicians, Vol. 1**, Seoul 2014.

[78]** On parameters for the group SO(2n)**, pages 1–29 in **Automorphic forms and related geometry: assessing the legacy of I. I. Piatetski-Shapiro**, Contemporary Mathematics, **614**, 2014.

[**MR3220921**: reviewed by Anton Deitmar]

[79]** Eigenfamilies, characters, and multiplicities**, Asterisque (2015), 1–25.

[80]**Germ expansions for real groups**, pages 1–91 in **Families of Automorphic Forms and the Trace Formula**, Simons Symposia, Springer, 2016.

[81]** Problems Beyond Endoscopy** (to appear in **Representation Theory, Number Theory and Invariant Theory**, Progress in Mathematics, Springer).

[82]**A stratification related to characteristic polynomials** (to appear in Advances in Mathematics, Birkhauser).

[83]**Functoriality and the Trace Formula** (submitted to **Geometric Aspects of the Trace Formula**, Simons Symposia, Springer).

[84]**Beyond Endoscopy and elliptic terms** pages 5–7 in **Harmonic Analysis and the Trace Formula**, Mathematisches Forschungsinstitut Oberwolfach, Report No 25/2017, 2017.

[85]**Memories of a Key Meeting** pages 23–26 in **The Fields Institute Turns 25**, edited by Elaine Mckinnon Riehm, Fields Institute for Research in Mathematical Sciences, 2017.