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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 show english descriptions Complex multiplication and moduli of abelian varieties [See also 14K22] 11G15 - Complex multiplication and moduli of abelian varieties [See also 14K22]
 

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