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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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On the Fejes Tóth problem about the sum of angles between lines
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by Dmitriy Bilyk and Ryan W. Matzke PDF
Proc. Amer. Math. Soc. 147 (2019), 51-59 Request permission

Abstract:

In 1959 Fejes Tóth posed a conjecture that the sum of pairwise nonobtuse angles between $N$ unit vectors in $\mathbb {S}^d$ is maximized by periodically repeated elements of the standard orthonormal basis. We obtain new improved upper bounds for this sum, as well as for the corresponding energy integral. We also provide several new approaches to the only settled case of the conjecture: $d=1$.
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Additional Information
  • Dmitriy Bilyk
  • Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55408
  • MR Author ID: 757936
  • Email: dbilyk@math.umn.edu
  • Ryan W. Matzke
  • Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55408
  • MR Author ID: 1115995
  • Email: matzk053@umn.edu
  • Received by editor(s): January 23, 2018
  • Published electronically: October 18, 2018
  • Additional Notes: This work is supported by the NSF grant DMS 1665007 (the first author) and the NSF Graduate Research Fellowship 00039202 (the second author)
  • Communicated by: Alexander Iosevich
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 51-59
  • MSC (2010): Primary 11K38, 52C35
  • DOI: https://doi.org/10.1090/proc/14263
  • MathSciNet review: 3876730