Geodesic
Values of the Dedekind Eta Function at Quadratic Irrationalities
Canadian journal of mathematics, Tome 51 (1999) no. 1, pp. 176-224

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Let $d$ be the discriminant of an imaginary quadratic field. Let $a$ , $b$ , $c$ be integers such that $${{b}^{2}}-4ac=d,a>0,\gcd (a,b,c)=1.$$ .The value of $\left| \eta ((b+\sqrt{d})/\left. 2a) \right| \right.$ is determined explicitly, where $\eta \left( z \right)$ is Dedekind’s eta function $$\eta (z)\,=\,{{e}^{\pi iz/12}}\,\prod\limits_{m=1}^{\infty }{(1-{{e}^{2\pi imz}})\,\,\,(im(z)>0).}$$
DOI : 10.4153/CJM-1999-011-1
Mots-clés : 11F20, 11E45, Dedekind eta function, quadratic irrationalities, binary quadratic forms, form class group 
Poorten, Alfred van der; Williams, Kenneth S. Values of the Dedekind Eta Function at Quadratic Irrationalities. Canadian journal of mathematics, Tome 51 (1999) no. 1, pp. 176-224. doi: 10.4153/CJM-1999-011-1
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