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Sur un théorème de M. Langevin. (On a theorem of M. Langevin). (French) Zbl 0641.12003
Michel Langevin proved the following result: Let V be a neighborhood of a point of the unit circle. There exists an effectively computable \(C>1\), such that any irreducible polynomial with integer coefficient set which has no root in V has a measure M(P)\(\geq C\) d, when its degree d is large enough. - His proof uses the notion of transfinite diameter.
Our proof proceeds in two steps: (i) construction of some multiple of P with “small” coefficients; \((ii)\quad application\) of a theorem of Erdős-Turan on the repartition of the roots of a polynomial over the complex numbers.
Reviewer: M.Mignotte

MSC:
11R04 Algebraic numbers; rings of algebraic integers
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