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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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