The determinant of the Eisenstein matrix and Hilbert class fields

Efrat, I.; Sarnak, P.

doi:10.1090/S0002-9947-1985-0792829-1

The determinant of the Eisenstein matrix and Hilbert class fields
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by I. Efrat and P. Sarnak PDF

Trans. Amer. Math. Soc. 290 (1985), 815-824 Request permission

Abstract:

We compute the determinant of the Eisenstein matrix associated to the Hilbert-Blumenthal modular group ${\text {PSL}_2}({\mathcal {O}_k})$, and express it in terms of the zeta function of the Hilbert class field of $K$.

References

Discrete groups and geometry

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Harmonic analysis on symmetric spaces with applications to number theory