Silver Jubilee Events

CMI Silver Jubilee Lecture Loic Merel, University of Paris VII, France
Friday, August 28, 2015
Consider a congruence subgroup D of degree zero supported
on C is torsion in the jacobian
of X. Depending on one's point of
view, one can see this result as
_{Γ}- either a part of the theory of special functions (one can
exhibit a rational function on
*X*whose divisor is a multiple of_{Γ}*D*) - or to the theory of automorphic forms. Find a
1-cycle
*c*on_{D}*X*with boundary_{Γ}*D*such that the integral of any holomorphic differential form along*c*vanishes. Such_{D}*c*can be characterized by its annihilation by certain Hecke operators._{D}
We adopt the latter point of view. The theorem of Manin and
Drinfeld amount to show that c, which should be
called an _{D}Eisenstein cycle, as it obeys similar
properties as Eisenstein series.
We will explain our approach to this problem and recent development due to D. Banerjee (Pune) and myself. |