Non-isotropic hausdorff capacity of exceptional sets of invariant potentials

1995 ◽  
Vol 4 (2) ◽  
pp. 141-155
Author(s):  
Manfred Stoll
Keyword(s):  
Exceptional Sets ◽  
Hausdorff Capacity

scholarly journals Non-isotropic Hausdorff capacity of exceptional sets for pluri-Green potentials in the unit ball of Cn

2006 ◽  
Vol 88 (1) ◽  
pp. 59-82
Author(s):  
Kuzman Adzievski
Keyword(s):  
Unit Ball ◽  
Exceptional Sets ◽  
Hausdorff Capacity ◽  
Green Potentials

On the exceptional sets concerning the leading partial quotient in continued fractions

2021 ◽  
Vol 500 (1) ◽  
pp. 125110
Author(s):  
Mengjie Zhang ◽  
Chao Ma
Keyword(s):  
Continued Fractions ◽  
Partial Quotient ◽  
Exceptional Sets

ON EXCEPTIONAL SETS: THE SOLUTION OF A PROBLEM POSED BY K. MAHLER

2016 ◽  
Vol 94 (1) ◽  
pp. 15-19 ◽  
Author(s):  
DIEGO MARQUES ◽  
JOSIMAR RAMIREZ
Keyword(s):  
Entire Functions ◽  
Complex Conjugation ◽  
Exceptional Set ◽  
Exceptional Sets ◽  
Transcendental Numbers ◽  
Lecture Notes ◽  
Transcendental Entire Functions

In this paper, we shall prove that any subset of $\overline{\mathbb{Q}}$, which is closed under complex conjugation, is the exceptional set of uncountably many transcendental entire functions with rational coefficients. This solves an old question proposed by Mahler [Lectures on Transcendental Numbers, Lecture Notes in Mathematics, 546 (Springer, Berlin, 1976)].

scholarly journals Homogeneous endpoint Besov space embeddings by Hausdorff capacity and heat equation

2006 ◽  
Vol 207 (2) ◽  
pp. 828-846 ◽  
Author(s):  
Jie Xiao
Keyword(s):  
Heat Equation ◽  
Besov Space ◽  
Hausdorff Capacity

scholarly journals Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem

2017 ◽  
Vol 15 (1) ◽  
pp. 1517-1529
Author(s):  
Zhao Feng
Keyword(s):  
Short Intervals ◽  
Exceptional Sets ◽  
Goldbach Problem ◽  
Almost All

Abstract In this paper, we are able to prove that almost all integers n satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 7, 8, i.e., $\begin{array}{} N=p_1^3+ \ldots +p_j^3 \end{array} $ with $\begin{array}{} |p_i-(N/j)^{1/3}|\leq N^{1/3- \delta +\varepsilon} (1\leq i\leq j), \end{array} $ for some $\begin{array}{} 0 \lt \delta\leq\frac{1}{90}. \end{array} $ Furthermore, we give the quantitative relations between the length of short intervals and the size of exceptional sets.

Exceptional sets related to the largest digits in Lüroth expansions

2021 ◽  
pp. 1-15
Author(s):  
Shuyi Lin ◽  
Jinjun Li ◽  
Manli Lou
Keyword(s):  
Number Theory ◽  
Hausdorff Dimension ◽  
Level Sets ◽  
Disjoint Union ◽  
Exceptional Set ◽  
Exceptional Sets ◽  
Lüroth Expansion

Let [Formula: see text] denote the largest digit of the first [Formula: see text] terms in the Lüroth expansion of [Formula: see text]. Shen, Yu and Zhou, A note on the largest digits in Luroth expansion, Int. J. Number Theory 10 (2014) 1015–1023 considered the level sets [Formula: see text] and proved that each [Formula: see text] has full Hausdorff dimension. In this paper, we investigate the Hausdorff dimension of the following refined exceptional set: [Formula: see text] and show that [Formula: see text] has full Hausdorff dimension for each pair [Formula: see text] with [Formula: see text]. Combining the two results, [Formula: see text] can be decomposed into the disjoint union of uncountably many sets with full Hausdorff dimension.

Exceptional sets for sums of five and six almost equal prime cubes

2018 ◽  
Vol 156 (2) ◽  
pp. 424-434 ◽  
Author(s):  
M. Wang
Keyword(s):  
Exceptional Sets
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