Height of flat tori

Chiu, Patrick

doi:10.1090/S0002-9939-97-03872-0

Height of flat tori
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Proc. Amer. Math. Soc. 125 (1997), 723-730 Request permission

Abstract:

Relations between the height and the determinant of the Laplacian on the space of $n$-dimensional flat tori and the classical formulas of Kronecker and Epstein are established. Extrema of the height are shown to exist, and results for a global minimum for 2-d tori and a local minimum for 3-d tori are given, along with more general conjectures of Sarnak and Rankin.

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