EVALUATION OF THE DEDEKIND ETA FUNCTION

Abstract. We extend the methods of Van der Poorten and Chapman [7] for explicitly evaluating the Dedekind eta function at quadratic irrationalities. Via Hecke L-series we obtain evaluations in some new cases. Specifically we provide further evaluations at points in imaginary quadratic number fields with class numbers up to four. We also describe techniques, which make use of modular equations, which provide additional evaluations not obtained via the L-series techniques, and we give a number of these evaluations explicitly here