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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Height of flat tori


Author: Patrick Chiu
Journal: Proc. Amer. Math. Soc. 125 (1997), 723-730
MSC (1991): Primary 11M36; Secondary 11F20, 11E45, 11H50, 11H55
MathSciNet review: 1396970
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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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Additional Information

Patrick Chiu
Affiliation: P.O. Box 7486, Palo Alto, California 94309

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03872-0
PII: S 0002-9939(97)03872-0
Received by editor(s): October 15, 1995
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 1997 American Mathematical Society