Atlas home ||
Conferences |
Abstracts |
about Atlas
Canadian Number Theory Association VIII Meeting
June 20-25, 2004
The Fields Institute
Toronto, ON, Canada |
|
Organizers
John Friedlander (Toronto) and Cam Stewart (Waterloo)
View Abstracts
Conference Homepage |
Arithmetic of Certain Hypergeometric Modular Forms
by
Karl Mahlburg
University of Wisconsin-Madison
Coauthors: Ken Ono (University of Wisconsin-Madison)
In a recent paper, Kaneko and Zagier studied a sequence
of modular forms Fk(z) which are solutions of a certain
second order differential equation. They studied the polynomials
|
|
~
F
|
k
|
(j)= |
Õ
\tau in H/\Gamma-{i, \omega}
|
(j-j(\tau))\ord\tau(Fk), |
|
where \omega = e2\pii/3 and H/\Gamma is the usual
fundamental domain of the action of SL2(\Z) on the upper half
of the complex plane. If p >= 5 is prime, they proved that
[F\tilde]p-1(j) mod p is the nontrivial factor of the
locus of supersingular j-invariants in
characteristic p. We consider the irreducibility of these
polynomials, and consider their Galois groups.
Date received: April 30, 2004
Copyright © 2004 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caok-24.