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# Evaluation of the Dedekind Eta Function

Published:2006-03-01
Printed: Mar 2006
• Robin Chapman
• William Hart
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## 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]

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