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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Height of flat tori
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by Patrick Chiu PDF
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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Additional Information
  • Patrick Chiu
  • Affiliation: P.O. Box 7486, Palo Alto, California 94309
  • Received by editor(s): October 15, 1995
  • Communicated by: Dennis A. Hejhal
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 723-730
  • MSC (1991): Primary 11M36; Secondary 11F20, 11E45, 11H50, 11H55
  • DOI: https://doi.org/10.1090/S0002-9939-97-03872-0
  • MathSciNet review: 1396970