| Affiliation: | 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 |
| 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. |
