Displaying similar documents to “Chebyshev bounds for Beurling numbers”

Transfinite diameter, Chebyshev constants, and capacities in ℂⁿ

Vyacheslav Zakharyuta (2012)

Annales Polonici Mathematici


The famous result of geometric complex analysis, due to Fekete and Szegö, states that the transfinite diameter d(K), characterizing the asymptotic size of K, the Chebyshev constant τ(K), characterizing the minimal uniform deviation of a monic polynomial on K, and the capacity c(K), describing the asymptotic behavior of the Green function g K ( z ) at infinity, coincide. In this paper we give a survey of results on multidimensional notions of transfinite diameter, Chebyshev constants and capacities,...

Smoothness of the Green function for a special domain

Serkan Celik, Alexander Goncharov (2012)

Annales Polonici Mathematici


We consider a compact set K ⊂ ℝ in the form of the union of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions g K is estimated. Markov’s constants of the corresponding set are evaluated.

Optimality of Chebyshev bounds for Beurling generalized numbers

Harold G. Diamond, Wen-Bin Zhang (2013)

Acta Arithmetica


If the counting function N(x) of integers of a Beurling generalized number system satisfies both 1 x - 2 | N ( x ) - A x | d x < and x - 1 ( l o g x ) ( N ( x ) - A x ) = O ( 1 ) , then the counting function π(x) of the primes of this system is known to satisfy the Chebyshev bound π(x) ≪ x/logx. Let f(x) increase to infinity arbitrarily slowly. We give a construction showing that 1 | N ( x ) - A x | x - 2 d x < and x - 1 ( l o g x ) ( N ( x ) - A x ) = O ( f ( x ) ) do not imply the Chebyshev bound.

Chebyshev Distance

Roland Coghetto (2016)

Formalized Mathematics


In [21], Marco Riccardi formalized that ℝN-basis n is a basis (in the algebraic sense defined in [26]) of [...] ℰTn T n and in [20] he has formalized that [...] ℰTn T n is second-countable, we build (in the topological sense defined in [23]) a denumerable base of [...] ℰTn T n . Then we introduce the n-dimensional intervals (interval in n-dimensional Euclidean space, pavé (borné) de ℝn [16], semi-intervalle (borné) de ℝn [22]). We conclude with the definition of Chebyshev distance [11]. ...