In 1959 Fejes Tóth posed a conjecture that the sum of pairwise nonobtuse angles between N unit vectors in 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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Received by the editors January 23, 2018. 2010 Mathematics Subject Classification. Primary 11K38, 52C35. This work is supported by the NSF grant DMS 1665007 (the first author) and the NSF Graduate Research Fellowship 00039202 (the second author).
© 2018, American Mathematical Society.