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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

The hexagonal versus the square lattice


Authors: Pieter Moree and Herman J.J. te Riele
Journal: Math. Comp. 73 (2004), 451-473
MSC (2000): Primary 11N13, 11Y35, 11Y60
Published electronically: June 11, 2003
MathSciNet review: 2034132
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

Pieter Moree
Affiliation: Korteweg–de Vries Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands
Email: moree@science.uva.nl

Herman J.J. te Riele
Affiliation: CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Email: herman@cwi.nl

DOI: http://dx.doi.org/10.1090/S0025-5718-03-01556-4
PII: S 0025-5718(03)01556-4
Received by editor(s): May 2, 2002
Received by editor(s) in revised form: August 6, 2002
Published electronically: June 11, 2003
Article copyright: © Copyright 2003 American Mathematical Society