Automorphic Forms Online References
This page is an incomplete, but evolving, list
of some online references for learning about
automorphic forms, representations and related topics. It is focused on
openaccess notes and survey papers, not research papers.
I may eventually add comments about each entry, and possibly will reorganize things by topic.
I'd like to make this into openedit database, but that may be awhile
in coming (or some energetic young person should volunteer to help with this),
so if there's something you'd like to add, please let me know.
Also, if you have suggestions for how the list (or future database)
should be better organized, I'd be happy to hear them.
Notes and Papers (organized by author)
 Automorphic representations and number theory, James Arthur, CMS Seminar (1981) 49pp.
 The trace formula and Hecke operators, James Arthur, Selberg volume (1989) 17pp.
 Lectures on automorphic Lfunctions, James Arthur and Stephen Gelbart (1991) 59pp.
 Harmonic analysis and group representations, James Arthur, Notices AMS (2000) 9pp.
 An introduction to the trace formula, James Arthur, Clay Volume (2005) 263pp.
 Report on the trace formula, James Arthur (2007) 12pp.
 A (very brief) history of the trace formula, James Arthur (2007) 11pp.
 The JacquetLanglands correspondence, Ioan Badulescu, TIFR Lectures (2001) 21pp.
 Automorphic forms lecture
notes, Ben Brubaker, 181pp.
 Relative aspects of the Langlands program lecture notes, Farrell Brumley (2021)
 On Some Applications of Automorphic Forms to Number Theory, Daniel Bump, Solomon Friedberg and Jeffrey Hoffstein, Bull. AMS (1996) 19pp.
 Notes on representations of GL(r) over a finite field, Daniel Bump, 15pp.
 Orbital integral and the Satake isomorphism, Daniel Bump (2004) 24pp.
 Lfunctions, Kevin Buzzard, TCC course notes (2008) 87pp.
 The infinite fern and families of quaternionic modular forms, Gaetan Chenevier,
Galois trimester course, IHP (2010)
 Analytic theory of Lfunctions for GL(n),
Langlands conjectures for GL(n), and
Dual groups and Langlands functoriality, James Cogdell, Jerusalem lectures (2001) 29pp., 18pp., 16pp.
 Converse theorems, functoriality and applications to number theory, James Cogdell and Ilya PiatetskiShapiro, ICM Proceedings, Beijing (2002) 10pp.
 Converse theorems, functoriality and applications, James Cogdell, Quart. J. (Borel volume, 2002), 27pp.
 Lfunctions and converse theorems for GL(n), James Cogdell, Park City Lecture Notes (2002) 85pp.
 Lectures on Lfunctions, converse theorems and functoriality for GL(n), James Cogdell, Fields Institute Lectures (2003) 109pp.
 Lecutres on integral representations of Lfunctions, James Cogdell, Columbia Workshop (2006) 23pp.
 An elementary introduction to the Langlands program, Stephen Gelbart, Bull. AMS (1984), 43pp.
 Lectures on automorphic Lfunctions, James Arthur and Stephen Gelbart (1991), 59pp.
 Lectures on the ArthurSelberg Trace Formula, Steven Gelbart, MSRI Lecture Notes (1995) 98pp.
 The
arithmetic of elliptic curves  an update, Benedict Gross, Arab J
(2009) 17pp.
 From Laplace to Langlands via representations of orthogonal groups,
Benedict Gross and Mark Reeder, Bull. AMS (2006), preprint version 60pp.
Exposition of local representations, packets
and GrossPrasad conjectures
 An introduction to the stable trace formula, Michael Harris, 40pp.
 Galois representations, automorphic forms, and the SatoTate conjecture, Michael Harris,
Clay research proceedings (2007), 33pp.
 Arithmetic
applications of the Langlands program, Michael Harris, Takagi lecture (2009), 61pp.
 Group representations and harmonic analysis from Euler to Langlands
[Part 2]
Anthony Knapp, Notices AMS (1996), 6pp. and 13pp.
 Introduction to the Langlands program,
Anthony Knapp, PSPM 61 (Edinburgh, 1997) 58pp.
 Theoretical aspects of the trace formula for GL(2),
Anthony Knapp, PSPM 61 (Edinburgh, 1997) 51pp.
 Applications of the trace formula,
Anthony Knapp and Jonathan Rogawski, PSPM 61 (Edinburgh, 1997) 19pp.
 Prerequisites for the Langlands program,
Anthony Knapp, Advanced Lectures in Mathematics (China, 2009) 9pp.
 First steps with the Langlands program,
Anthony Knapp, Advanced Lectures in Mathematics (China, 2009) 12pp.
 Introduction
to endoscopy, JeanPierre Labesse, Snowbird Lectures (2006) 54pp.
 A motivated introduction to the Langlands program, M. Ram Murty, Advances in Number Theory (1993), 30pp.
 Selberg's conjectures and Artin Lfunctions, M. Ram Murty, Bull. AMS (1994), 14pp.
 Recent Developments in the Langlands program, M. Ram Murty, CR Math Acad Sci Can (2002) 22pp.
 Lectures on symmetric power Lfunctions, M. Ram Murty, Fields Institute Lecture Notes (2004) 81pp.
 Endocsopic theory of
automorphic forms, Ngo Bau Chau, ICM 2010, 28pp.
 An introduction to the
local Langlands correspondence, Mark Reeder (2012), 26pp.
 From Laplace to Langlands via representations of orthogonal groups,
Benedict Gross and Mark Reeder, Bull. AMS (2006), preprint version 60pp.
Exposition of local representations, packets
and GrossPrasad conjectures
 Functoriality and the Artin conjecture, Jonathan Rogawski, PSPM 61 (Edinburgh, 1997) 23pp.
 Applications of the trace formula,
Anthony Knapp and Jonathan Rogawski, PSPM 61 (Edinburgh, 1997) 19pp.
 The nonabelian reciprocity law for local fields, Jonathan Rogawski, Notices AMS (2000) 7pp.
 Automorphic forms course page, Yiannis Sakellaridis
 Serre's Modularity Conjecture,
Michael Schein, Winter School on Galois Theory notes (Luxembourg, 2012) 26pp.
 Galois Representations [long version] [short version], Richard Taylor, ICM Lecture (2002), 42pp. and 25pp.
 Reciprocity laws and
density theorems, Richard Taylor, Shaw lecture (for a general audience)
(2007) 19pp.
 (Classical) Automorphic
forms course page, Holger Then (2012)
 Automorphic forms and
Langlands program, Yannan Qiu, course notes taken by Robert Rhoades (2008)
136pp.
 An elementary
introduction to the local trace formulas of J. Arthur. The case of finite
groups, MarieFrance Vigneras (1991) 19pp.
 Introduction to the Langlands modulo p correspondence for GL(2,Q_p), MarieFrance
Vigneras, Princeton lectures (2010) 20pp.
 Introductory
lectures on automorphic forms, Nolan Wallach, Luminy Summer School (2001)
84pp.
 Advanced
Number Theory, Jared Weinstein course notes (2011)
Background material for and brief intro to
automorphic representations
Classic Collections
Recent Collections
 LMFDB's list of lecture notes (number theory, elliptic curves, modular forms and
automorphic forms)

Arizona Winter School
Yearly weeklong school on topics in arithmetic
geometry with notes and videos

Clay Summer School on Galois Representations (Honolulu, 2009)
Notes by Brinon and Conrad on padic Hodge theory,
Kisin and Tilouine on deformation theory, Bellaiche on
Iwasawa theory
 Galois Trimester, Institut Henri Ponicare, Jan. 4  Mar. 27, 2010
Link appears to be broken
 Hakuba 2006 Proceedings (on GSp(4))
Notes from both introductory and research talks
 Heegner Points and Rankin LSeries (MSRI Volume 49)
A mix of introductory and research talks
 Papers and Talks on Random Matrix Theory and Lfunctions from the
2009 Graduate Workshop on Zeta Functions, LFunctions and their Applications
Notes by Conrey on random matrices, Murty on Artin Lseries, and Gonek on the Riemann zeta function
 Representation theory
of real reductive Lie groups (Casselman/Milicic conference), Snowbird,
Utah, Jun 48, 2006
Notes by Adams on real groups, Labesse on endoscopy, MillerSchmid on RankinSelberg and Arthur's problems for real groups
 Stanford number theory seminars, listed on
Brian Conrad's webpage
Notes from yearlong learning seminars on topics
such as modularity lifting and work of Mordell, Darmon and Shimura
 Trieste (ICTP) School
on Automorphic Forms on GL(n), 2000 (ICTP Lectures Vol 21)
Notes by Raghunathan, Venkataramana, Cogdell,
PrasadRaghuram, Harder and Wedhom
 Trieste (ICTP) Summer School on Automorphic forms and Shimura Varieties, 2007 (some
lecture notes available)
Notes by Nair, Henniart, Venkataramana, Prasad,
Rajan, Edixhoven, Chaudouard, Yu, Jiang
 Kevin Buzzard's notes in a similar spirit to Paul Garrett's vignettes
 Chao Li, a Harvard
grad student with various notes online (e.g., this and
this)
 Michael Woodbury (notes from some courses, conferences, etc)
Kimball Martin
Wed Jan 5 22:24:23 EST 2022
kimball.martin@ou.edu