Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions
Communications in Mathematics, Tome 13 (2005) no. 1, pp. 13-18
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library
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 \[ k = [f_1 (n_1)]+ [f_2 (n_2)]+ \dots + [f_m(n_m)]. \]
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 \[ k = [f_1 (n_1)]+ [f_2 (n_2)]+ \dots + [f_m(n_m)]. \]
@article{COMIM_2005_13_1_a1,
author = {Jahoda, Pavel and P\v{e}luchov\'a, Monika},
title = {Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions},
journal = {Communications in Mathematics},
pages = {13--18},
year = {2005},
volume = {13},
number = {1},
mrnumber = {2290414},
zbl = {1207.11020},
language = {en},
url = {http://geodesic.mathdoc.fr/item/COMIM_2005_13_1_a1/}
}
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 - Communications in Mathematics PY - 2005 SP - 13 EP - 18 VL - 13 IS - 1 UR - http://geodesic.mathdoc.fr/item/COMIM_2005_13_1_a1/ LA - en ID - COMIM_2005_13_1_a1 ER -
%0 Journal Article %A Jahoda, Pavel %A Pěluchová, Monika %T Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions %J Communications in Mathematics %D 2005 %P 13-18 %V 13 %N 1 %U http://geodesic.mathdoc.fr/item/COMIM_2005_13_1_a1/ %G en %F COMIM_2005_13_1_a1
Jahoda, Pavel; Pěluchová, Monika. Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions. Communications in Mathematics, Tome 13 (2005) no. 1, pp. 13-18. http://geodesic.mathdoc.fr/item/COMIM_2005_13_1_a1/
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[2] Landau E.: Über die Einteilung der ...Zahlen in 4 Klassen .. Arch. Math. Phys. (3), 13 (1908) 305–312.
[3] Jahoda P.: Notes on the expression of natural numbers as sum of powers. Tatra Mt. Math. Publ. 34 (2005), 1–11, Bratislava, Mathematical Institute Slovak Academy of Sciences. | MR | Zbl