Dynamical Zeta function of the β -shift for β a totally real algebraic number. The Bogomolov Property
Résumé
The dynamical zeta function of the beta-shift is used to prove the following result: Let Qtr denote the field of all totally real numbers. If h denotes the absolute logarithmic Weil height, α ∈ Qtr , α \not= 0, \not= ±1 ⇒ h(α) > 1/4 x Log ((θ_(31) ) ^(−1)) = 0.020498 . . . where θ_(31) is the unique zero of the trinomial -1+x+x^(31).
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