The hexagonal versus the square lattice

Authors:
Pieter Moree;Herman J. J. te Riele
Affiliations:
Korteweg-De Vries Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands;CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Venue:
Mathematics of Computation
Year:
2004

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ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part I

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Abstract

Schmutz Schaller's conjecture regarding the lengths of the hexagonal versus the lengths of the square lattice is shown to be true. The proof makes use of results from (computational) prime number theory.Using an identity due to Selberg, it is shown that, in principle, the conjecture can be resolved without using computational prime number theory. By our approach, however, this would require a huge amount of computation.