Benjamin Kane (DIAMANT postdoc at RU Nijmegen): Representations
of Integers by Ternary Quadratic Forms and CM Lifts of Supersingular
Elliptic Curves
In this talk, we will show an explicitly computable bound D_theta such
that every integer D>D_theta is represented by a quadratic form theta
if and only if it is locally represented. The bound will depend on
certain Generalized Riemann Hypotheses. Using a connection to lifts of
supersingular elliptic curves, we will also see that the reduction map
from elliptic curves with CM by O_{-D} is surjective whenever D>D_theta.
In certain cases, this bound is feasible, and we will use a computer
to find the full list of D which are not represented by the given form
or equivalently, for which the reduction map is not surjective.