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2001 Hermite's Constant for Quadratic Number Fields
Ricardo Baeza, Renaud Coulangeon, Maria Ines Icaza, Manuel O'Ryan
Experiment. Math. 10(4): 543-552 (2001).


We develop a method to compute the Hermite-Humbert constants $\gam_{K,n}$ of a real quadratic number field $K$, the analogue of the classical Hermite constant $\gam_n$ when $\funnyQ$ is replaced by a quadratic extension. In the case $n=2$, the problem is equivalent to the determination of lowest points of fundamental domains in $\H^2$ for the Hilbert modular group over $K$, that had been studied experimentally by H. Cohn. We establish the results he conjectured for the fields $ \funnyQ@(\sqrt{2})$, $\funnyQ@(\sqrt{3})$ and $\funnyQ@(\sqrt{5})$. The method relies on the characterization of extreme forms in terms of perfection and eutaxy given by the second author in an earlier paper.


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Ricardo Baeza. Renaud Coulangeon. Maria Ines Icaza. Manuel O'Ryan. "Hermite's Constant for Quadratic Number Fields." Experiment. Math. 10 (4) 543 - 552, 2001.


Published: 2001
First available in Project Euclid: 26 November 2003

zbMATH: 1042.11045
MathSciNet: MR1881755

Rights: Copyright © 2001 A K Peters, Ltd.


Vol.10 • No. 4 • 2001
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