Sommersemester 2009 - Forschungsseminar on p-adic L-functions

• Date: Thursday, 10-12 a.m.
• Place: T03 R04 D10
• Starting date: 16 April 2009
• The language of the seminar will be English.
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Description

In this seminar we study the construction of p-adic L-functions attached to modular forms and advance in the direction of the Mazur-Tate-Teitelbaum conjecture, a proof of which is just out of reach at the end of the seminar.

Organisers

Gebhard Böckle and Gabor Wiese

Programme

Latest version of the programme.

List of Lectures

	Date	Speaker	Title
1	16/04/2009	Ambrus Pál (Imperial College, London)	Complex valued L-functions
2	23/04/2009	Haluk Sengün	The periods of a newform
3	30/04/2009	Adam Mohamed	Continuous functions and measures on Z_p
4	07/05/2009	Pietro Ploner	The Leopoldt-Kubota p-adic zeta-function and more functions
5	14/05/2009	Doan Trung Cuong	Locally analytic functions and distributions
	28/05/2009	--	(no talk)
6	04/06/2009	Stefan Kukulies	The p-adic L-functions of modular forms and elliptic curves
7	18/06/2009	Yamidt Tobon Bermudez	The p-adic upper half plane
8	25/06/2009	Björn Buth	Morita duality
9	02/07/2009	Ralf Butenuth	The Poisson kernel and harmonic cochains
10	16/07/2009	Juan Marcos Cervino	Modular symbols and Teitelbaum's L-invariant
11	23/07/2009	Johan Bosman	Harmonic modular symbols and the L-invariant of Orton

References

• M. Bertolini, H. Darmon, P. Green. Periods and points attached to quadratic algebras in "Heegner points and Rankin L-series", 323--367, MSRI Publ. 49, Cambridge Univ. Press, Cambridge, 2004.
• P. Colmez. Fontaine's rings and p-adic L-functions. Course given at Tsinghua University during the fall of 2004.
• P. Colmez. Zéros supplémentaires de fonctions L p-adiques de formes modulaires. Algebra and number theory, 193--210, Hindustan Book Agency, Delhi, 2005.
• P. Colmez. La conjecture de Birch et Swinnerton-Dyer p-adique. Astérisque 294 (2004), ix, 251--319.
• P. Colmez. Fonctions L p-adiques. Séminaire Bourbaki, 1998/99. Astérisque 266 (2000), Exp. No. 851, 3, 21--58.
• F. Diamond, J. Shurman. A first course in modular forms. GTM 228. Springer-Verlag, New York, 2005.
• S. Dasgupta, J. Teitelbaum. The p-adic upper half plane. Lectures for the 2007 Arizona Winter School.
• J. Fresnel, M. van der Put. Géométrie analytique rigide et applications. Boston: Birkhäuser 1981.
• N. Koblitz. p-adic numbers, p-adic analysis, and zeta-functions. GTM 58. Springer-Verlag, New York, 1984.
• B. Mazur, P. Swinnerton-Dyer. Arithmetic of Weil curves. Invent. Math. 25 (1974), 1--61.
• B. Mazur, J. Tate, J. Teitelbaum. On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer. Invent. Math. 84 (1986), no. 1, 1--48.
• L. Orton. An elementary proof of a weak exceptional zero conjecture. Canad. J. Math. 56 (2004), no. 2, 373--405.
• J. Silverman. Advanced topics in the arithmetic of elliptic curves. GTM 151. Springer-Verlag, New York, 1994.
• J. Silverman. The arithmetic of elliptic curves. GTM 106. Springer-Verlag, New York, reprint 1992.

Last modification: 7 October 2009.