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Evaluation of the Dedekind Eta Function

Published online by Cambridge University Press:  20 November 2018

Robin Chapman  and
William Hart
Robin Chapman
Affiliation:
Department of Mathematical Sciences, University of Exeter, EX4 4QE, UK e-mail: rjc@maths.ex.ac.uk
William Hart
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A. e-mail: wbhart@math.uiuc.edu
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Abstract

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We extend the methods of Van der Poorten and Chapman for explicitly evaluating the Dedekind 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.

Keywords

11G15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 1 , 01 March 2006 , pp. 21 - 35
Copyright
Copyright © Canadian Mathematical Society 2006

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