BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:CM values of Green’s functions
DTSTART;VALUE=DATE-TIME:20131119T143000Z
DTEND;VALUE=DATE-TIME:20131119T150000Z
DTSTAMP;VALUE=DATE-TIME:20211128T115147Z
UID:indico-event-404@indico.math.cnrs.fr
DESCRIPTION:A classical result of Kronecker and Weber states that the valu
e of the elliptic j-function at a point of complex multiplication (i.e. a
point lying in the intersection of the upper half-plain and some imaginary
quadratic field) is algebraic. B. Gross and D. Zagier have conjectured th
at a similar phenomenon also holds for certain modular eigenfunctions of t
he hyperbolic Laplace operator. Namely\, the higher Green's functions are
real-valued functions of two variables on the upper half-plane which are b
i-invariant under the action of SL2(Z)\, have a logarithmic singularity al
ong the diagonal and are eigenfunctions of the hyperbolic Laplace operator
with eigenvalue k(1-k) for some positive integer k. The conjecture formul
ated in "Heegner points and derivatives of L-series'' (1986) predicts when
the value of a higher Green's function at a pair of points of complex mul
tiplication is equal to the logarithm of an algebraic number. In this talk
I would like to present a proof of this conjecture for a pair of points b
oth lying in the same imaginary quadratic field.\n\nhttps://indico.math.cn
rs.fr/event/404/
LOCATION:IHES Amphitéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/404/
END:VEVENT
END:VCALENDAR