Modular symbols and their applications

任课教师:Emmanuel Lecouturier
时间: 每周四09:50-11:25, 2019-9-12 ~ 11-7


Modular symbols are various (co)homology groups related to congruence subgroups of SL_2(Z). We have finite presentations for these groups, e.g. the Manin symbols. Their close relation to modular forms and their explicit nature make them a powerful tool. In this course, we will study modular symbols and some applications (e.g. to elliptic curves, Hecke algebras, Lfunctions…). We will rely on the work of Loïc Merel.


Basic properties of singular (co)homology. It is better to have some notions on modular forms and Hecke algebras, although I will recall what we need.


[1] William Stein « Modular Forms:A Computational Approach » (DOI:10.1090/gsm/079);

[2] Loïc Merel: « Universal Fourier expansions of modular forms » (DOI: 10.1007/BFb0074110);

[3] Loïc Merel: « Symboles de Manin et valeurs de fonctions L » (DOI:10.1007/978-0-8176-4747-6_9);

[4] Loïc Merel: « L'accouplement de Weil entre le sous-groupe de Shimura et le sous-groupe cuspidal de J_0(p) » (DOI: 10.1515/crll. 1996.477.71).

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