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- W1631701233 abstract "Concentration and equi-distribution, near the unit circle, in Solo- myak's set, of the union of the Galois conjugates and the beta-conjugates of a Parry number fl are characterized by means of the Erd}os-Turan approach, and its improvements by Mignotte and Amoroso, applied to the analytical function ffl(z) = i1+ P i‚1 tiz i associated with the Renyi fl-expansion dfl(1) = 0:t1t2 ::: of unity. Mignotte's discrepancy function requires the knowledge of the factor- ization of the Parry polynomial of fl. This one is investigated using theorems of Cassels, Dobrowolski, Pinner and Vaaler, Smyth, Schinzel in terms of cyclo- tomic, reciprocal non-cyclotomic and non-reciprocal factors. An upper bound of Mignotte's discrepancy function which arises from the beta-conjugates of fl which are roots of cyclotomic factors is linked to the Riemann hypothesis, following Amoroso. An equidistribution limit theorem, following Bilu's theorem, is formu- lated for the concentration phenomenon of conjugates of Parry numbers near the unit circle. Parry numbers are Perron numbers. Open problems on non-Parry Perron numbers are mentioned in the context of the existence of non-unique fac- torizations of elements of number flelds into irreducible Perron numbers (Lind)." @default.
- W1631701233 created "2016-06-24" @default.
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- W1631701233 date "2009-03-03" @default.
- W1631701233 modified "2023-09-27" @default.
- W1631701233 title "Uniform distribution of Galois conjugates and beta-conjugates of a Parry number near the unit circle and dichotomy of Perron numbers" @default.
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