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Kenneth Williams - Values of the Dedekind eta function at quadratic irrationalities



KENNETH WILLIAMS, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario  K1S 5B6, Canada
Values of the Dedekind eta function at quadratic irrationalities


The Dedekind eta function $\eta(z)$ is defined by

\begin{displaymath}\eta (z) = e^{\pi i z/12} \prod^\infty_{m=1} (1-e^{2\pi imz})
\end{displaymath}

for im (z) >0. Let d be the discriminant of an imaginary quadratic field. The value of $\bigl\vert \eta \bigl((b +\sqrt{d}/2a\bigr)\bigr\vert$is determined for integers a, b, c satisfying

\begin{displaymath}b^2 -4ac = d, \quad a >0, \ (a,b,c) =1.
\end{displaymath}

This is joint work with A. J. van der Poorten.



 

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