Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions

Jahoda, Pavel, and Pěluchová, Monika. "Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions." Acta Mathematica Universitatis Ostraviensis 13.1 (2005): 13-18. <http://eudml.org/doc/35148>.

@article{Jahoda2005,
abstract = {This paper generalizes some results from another one, namely [3]. We have studied the issues of expressing natural numbers as a sum of powers of natural numbers in paper [3]. It means we have studied sets of type $A = \lbrace n_1^\{ k_1\}+n_2^\{ k_2\}+ \dots + n_m^\{ k_m\} \mid n_i \in \mathbb \{N\}\cup \lbrace 0 \rbrace , i = 1, 2 \dots , m, (n_1, n_2, \dots ,n_m) \ne (0,0, \dots , 0 )\rbrace , $ where $k_1, k_2, \dots , k_m \in \mathbb \{N\}$ were given natural numbers. Now we are going to study a more general case, i.e. sets of natural numbers that are expressed as sum of integral parts of functional values of some special functions. It means that we are interested in sets of natural numbers in the form \[ k = [f\_1 (n\_1)]+ [f\_2 (n\_2)]+ \dots + [f\_m(n\_m)]. \]},
author = {Jahoda, Pavel, Pěluchová, Monika},
journal = {Acta Mathematica Universitatis Ostraviensis},
keywords = {Asymptotic density; sum of integral parts of functional values of some special functions},
language = {eng},
number = {1},
pages = {13-18},
publisher = {University of Ostrava},
title = {Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions},
url = {http://eudml.org/doc/35148},
volume = {13},
year = {2005},
}

TY - JOUR
AU - Jahoda, Pavel
AU - Pěluchová, Monika
TI - Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions
JO - Acta Mathematica Universitatis Ostraviensis
PY - 2005
PB - University of Ostrava
VL - 13
IS - 1
SP - 13
EP - 18
AB - This paper generalizes some results from another one, namely [3]. We have studied the issues of expressing natural numbers as a sum of powers of natural numbers in paper [3]. It means we have studied sets of type $A = \lbrace n_1^{ k_1}+n_2^{ k_2}+ \dots + n_m^{ k_m} \mid n_i \in \mathbb {N}\cup \lbrace 0 \rbrace , i = 1, 2 \dots , m, (n_1, n_2, \dots ,n_m) \ne (0,0, \dots , 0 )\rbrace , $ where $k_1, k_2, \dots , k_m \in \mathbb {N}$ were given natural numbers. Now we are going to study a more general case, i.e. sets of natural numbers that are expressed as sum of integral parts of functional values of some special functions. It means that we are interested in sets of natural numbers in the form \[ k = [f_1 (n_1)]+ [f_2 (n_2)]+ \dots + [f_m(n_m)]. \]
LA - eng
KW - Asymptotic density; sum of integral parts of functional values of some special functions
UR - http://eudml.org/doc/35148
ER -