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Evaluation of the Dedekind Eta Function |
Canad. Math. Bull. 49(2006), 21-35
Published:2006-03-01
Printed: Mar 2006
Printed: Mar 2006
- Robin Chapman
- William Hart
Abstract
We extend the methods of Van der Poorten and Chapman
for
explicitly evaluating the Dede\-kind eta function at quadratic
irrationalities. Via evaluation of Hecke
$L$-series we obtain new evaluations at points in
imaginary quadratic number fields with
class numbers 3 and 4. Further, we overcome the limitations
of the earlier methods and via modular equations provide
explicit evaluations where the class number is 5 or 7.
| MSC Classifications: | 11G15 - Complex multiplication and moduli of abelian varieties [See also 14K22] |