Next: I. Nikolaev - 3-manifolds,
Up: Contributed Papers Session /
Previous: Contributed Papers Session /
ALEXANDRU GICA, Faculty of Mathematics, University of Bucharest,
RO-70109 Bucharest 1, Romania |
A conjecture which implies the theorem of
Gauss-Heegner-Stark-Baker |
In 1801 Gauss conjectured that the ring of integers for a quadratic
imaginary field
is principal only for a finite
number of d. Heegner, Stark and Baker proved that only for
-d=1,2,3,7,11,19,43,67,163
the ring of integers for
(where
,
d<0,
d squarefree) is principal. We prove two result which are
equivalent with this theorem and we pose a conjecture which implies
the
Gauss-Heegner-Stark-Baker theorem (we will abbreviate: the G.H.S.B.
theorem). Finally we pose a ``weaker'' conjecture which seems to be
more approachable than the other one.