Student Seminar: Number Theory and Automorphic Forms

Organizers: Lior Silberman, Bill Casselman, Julia Gordon.

Contact: lior

@

math.ubc.ca

; MATH 229B

; 604-827-3031

Fall 2008: Real-Analytic forms and Eisenstein Series

Meetings: Thursdays, 10-12:30 at WMAX 110 (PIMS large seminar room)
Reading Course number: 620D ("topics in number theory")
Syllabus (PDF)
Organizational meeting: Tuesday, September 2nd, 3-4pm in MATX 1102.
No meeting 4/9 (TA training & Dept Luncheon).
Tuesday 7/10: 15:00-17:00 meeting at WMAX 216 (9/10 is Yom Kippur).
No meeting 30/10 (Lior & Bill out of town).

Agenda

Meeting	Title	Speaker	Notes & References
1. (2/9)	Holomorphic forms	Lior Silberman	[7]
2. (11/9)	Hilbert spaces and self-adjoint operators	Bill Casselman	[6]
3. (18/9)	Hyperbolic geometry	Hesam Abbaspour
4. (25/9)	Hyperbolic geometry Maass forms	Lior Silberman Scott Sitar	notes [3]
5. (2/10)	Absolute convergence of Eisenstein series	Alia Hamieh	[5]
6. (7/10)	Compact operators and the resolvent Analytical continuation of Eisenstein series	Lior Silberman Jay Heumann	[2] [4]
7. (16/10)	The analytical continuation (ctd) Representation Theory of SL_2(R)	Jay Heumann Julia Gordon
8. (23/10)	Representation Theory of SL_2(R), continued	Julia Gordon
9. (6/11)	Maass forms associated to real quadratic fields L-functions associated to Maass forms	Hesam Abbaspour
10. (13/11)	Hecke operators the Euler product	Scott Sitar	[1]
11. (20/11)	Adeles and adelic groups	Jay Heumann
12. (27/11)	The adelic perspective	Alia Hamieh	[1]

References

	Topics	Author(s)	Title	Data
[1]		Bump	Automorphic forms and representations	CSM No. 53. Cambridge University Press, Cambridge, 1997. xiv+574 pp. ISBN: 0-521-55098-X, MR: 1431508
[2]	Continuation of E. Series	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. MR: 0639175
[3]	Maass forms, the space Γ\H	Iwaniec	Spectral Methods of Automorphic Forms	2nd edition. GSM No. 53. AMS, Providence, RI, 2002. xii+220 pp. ISBN: 0-8218-3160-7, MR: 1942691
[4]	Continuation of E. Series	Jacquet	Note on the analytic continuation of Eisenstein series	Proc. Sympos. Pure Math. 61 (1997), 407–412. MR: 1476506
[5]	Convergence of E. series	Kubota	Elementary theory of Eisenstein series	Halsten Press, New York, 1973. xi+110 pp. MR: 0429749
[6]	Hilbert spaces, Elliptic Regularity, Fourier Analysis	Reed and Simon	Methods of modern mathematical physics I: Functional analysis	2nd edition. Academic Press, New York, 1980. xv+400 pp. ISBN: 0-12-585050-6, MR: 0751959
[7]	Quadratic forms and modular forms	Serre	A Course in Arithmetic	GTM No. 7. Springer-Verlag, New York-Heidelberg, 1973. viii+115 pp. ISBN: 0-38-7900403-0, MR: 0255476

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Last modified Friday August 07, 2009