130 and the Cube Spectrum

Eberhard R. Hilf   Phone: +49-(0)441-798-2542   Fax: +49-(0)441-798-3201
H. P. Baltes


Date: 1973

Article: unpublished

The asymptotic mean degeneracy and spacing of the eigenvalue spectrum of the wave 
equation for a cube-shaped domain is presented. This could be achieved by realizing
the following new property of the number 130. It is conjectured that there exist
just 10 numbers, which can neither be represented as (i) a sum of three positive 
squares, nor as (ii) 4^a ( 8b+7 ), and which (iii) are not multiples of 4. 130 is
the largest of these 10 numbers. This conjecture was checked numerically for numbers 
up to 40,000.

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Metadata by Thomas Severiens on 13 April 1999
Supporting work done by Sandra Valeska Bergmann.