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The Fekete-Szegő theorem with splitting conditions. II. (English) Zbl 1126.11342
Summary: We prove a theorem of Fekete-Szegő-Robinson type for affine adelic sets over a number field \(K\), which asserts that for a set with capacity greater than \(1\), every adelic neighborhood of the set contains infinitely many Galois orbits of algebraic numbers. For a finite number of places \(v\), if the \(v\)-component of the set is contained in \(K_v\), then the algebraic numbers produced will have all their conjugates in \(K_v\).
For part I, see Acta Arith. 93, No. 2, 99–116 (2000; Zbl 0946.11025).

MSC:
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
11R56 Adèle rings and groups
12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
31C15 Potentials and capacities on other spaces
11R04 Algebraic numbers; rings of algebraic integers
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