PIROSKA LAKATOS
On a number theoretical application of Coxeter transformations
Pages: 293-301
Received: 22 August 2000
Mathematics Subject Classification (2000): 11R06 - 05C05 - 20F55
Research partially supported by Hungarian NFSR grant No. TO 29525
Abstract: We show that the spectral radii of the Coxeter transformation of wild stars are Salem numbers and their suitable limits are PV-numbers. The link between these limits and PV-numbers is the polynomial F(x)=x k+1-(s-1) (xk+1-1)/(x-1). The fact that the largest positive zero &eta of F is a PV-number follows from the theory of the first derived set of PV-numbers given in Chapter 6 in [1]. We give an elementary proof of this result and also show how &eta can be located : s-s -k < η < s-s-k-1 where s+1 is the number of all arms of the wild star and k is the length of the arm that remains fixed during the limiting process.