Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Friday, 2 September 2005, 11:00 - 11:45, Plexus Spectrumzaal.

Loic Merel: The formula relating modular symbols to L-values.

Abstract: There are well known formulas relating values of L-functions of modular forms to modular symbols. These formulas enable to construct p-adic L-functions etc. Modular symbols contain a finite generating set consisting of the so-called Manin symbols. I will describe how one can express a Manin symbol at level N in terms of L-values obtained by twisting modular forms of level N by characters of level dividing N and of a few local invariants. Here is an elementary corollary of this formula: the regular representation of Gal(Q(\mu_N)/Q), where Q(\mu_N) is the field generated by a primitive N-th root of unity, does not occur in the group of Q(\mu_N)-rational points of an elliptic curve E over Q of conductor N.