$f$- transfinite diameter and number theoretic applications
نویسندگان
چکیده
منابع مشابه
Transfinite Diameter
The transfinite diameter is a way of quantifying the size of compact sets in Euclidean space. This quantity is related to the Hausdorff dimension and the Lebesgue measure, but gives a slightly different perspective on the set than either of those do. In this paper, we introduce the transfinite diameter, and outline some attempts to calculate this quantity for three sets in R. For z1, z2, . . . ...
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We prove a formula for the Fekete-Leja transfinite diameter of the pullback of a set E ⊂ C by a regular polynomial map F , expressing it in terms of the resultant of the leading part of F and the transfinite diameter of E. We also establish the nonarchimedean analogue of this formula. A key step in the proof is a formula for the transfinite diameter of the filled Julia set of F .
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We study the problem of finding nonconstant monic integer polynomials, normalized by their degree, with small supremum on an interval I. The monic integer transfinite diameter tM(I) is defined as the infimum of all such supremums. We show that if I has length 1, then tM(I) = 1 2 . We make three general conjectures relating to the value of tM(I) for intervals I of length less than 4. We also con...
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Explicit auxiliary functions can be used in the “Schur-SiegelSmyth trace problem”. In the previous works, these functions were constructed only with polynomials having all their roots positive. Here, we use several polynomials with complex roots, which are found with Wu’s algorithm, and we improve the known lower bounds for the absolute trace of totally positive algebraic integers. This improve...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1993
ISSN: 0373-0956
DOI: 10.5802/aif.1368