Student Seminar: Number Theory and Automorphic Forms

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]

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

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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