Characterization of zeta functions of SFTs
by
Nicholas Ormes
Univ. of Texas, Austin
Coauthors: Mike Boyle, Ki Hang Kim, Fred Roush

Let S be a unital subring of the reals and let p(t) be a polynomial with coefficients in S and constant term 1. The Spectral Conjecture of Boyle and Handelman asserts that given certain necessary conditions (Perron and tracial), there is a primitive matrix over S with characteristic polynomial of the form t^k[p(1/t)]. We prove the conjecture for S=Z. This result characterizes the zeta functions of mixing shifts of finite type (SFTs), and easily yields a characterization of the zeta functions of arbitrary SFTs.

Date received: March 18, 1998