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Alexandru Gica - A conjecture which implies the theorem of Gauss-Heegner-Stark-Baker
| 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.
