The hexagonal versus the square lattice

Moree, Pieter; te Riele, Herman

doi:10.1090/S0025-5718-03-01556-4

The hexagonal versus the square lattice
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by Pieter Moree and Herman J.J. te Riele PDF

Math. Comp. 73 (2004), 451-473 Request permission

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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