scholarly journals On additive representation functions

2018 ◽  
Vol 93 (1-2) ◽  
pp. 205-213
Author(s):  
Yong-Gao Chen ◽  
Hui Lv
Keyword(s):  
Additive Representation

On the k-th difference of an additive representation function

2011 ◽  
Vol 48 (1) ◽  
pp. 93-103
Author(s):  
Sándor Kiss
Keyword(s):  
Infinite Sequence ◽  
Probabilistic Methods ◽  
Number Of Solutions ◽  
Fixed Integer ◽  
Representation Function ◽  
Additive Representation ◽  
Consecutive Integers ◽  
Additive Representation Function ◽  
Positive Integers

Let k ≧ 2 be a fixed integer, A = {a1, a2, …} (a1 < a2 < …) be an infinite sequence of positive integers, and let Rk(n) denote the number of solutions of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$a_{i_1 } + a_{i_2 } + \cdots + a_{i_k } = n,a_{i_1 } \in \mathcal{A},...,a_{i_k } \in \mathcal{A}$$ \end{document}. Let B(A, N) denote the number of blocks formed by consecutive integers in A up to N. In [5], it was proved that if k > 2 and \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\lim _{N \to \infty } \frac{{B(\mathcal{A},N)}}{{\sqrt[k]{N}}}$$ \end{document} = ∞ then |δl(Rk(n))| cannot be bounded for l ≦ k. The aim of this paper is to show that the above result is nearly best possible. We are using probabilistic methods.

scholarly journals Additive representation in thin sequences, II: The binary Goldbach problem

Mathematika ◽  
2000 ◽  
Vol 47 (1-2) ◽  
pp. 117-125 ◽  
Author(s):  
J. Brüdern ◽  
K. Kawada ◽  
T. D. Wooley
Keyword(s):  
Additive Representation ◽  
Goldbach Problem

Properties of an atom–bond additive representation of the interaction for benzene–argon clusters

2004 ◽  
Vol 392 (4-6) ◽  
pp. 514-520 ◽  
Author(s):  
M Albertı́ ◽  
A Castro ◽  
A Laganà ◽  
F Pirani ◽  
M Porrini ◽  
...  
Keyword(s):  
Additive Representation ◽  
Argon Clusters ◽  
Atom Bond

scholarly journals Additive representation in thin sequences, V: Mixed problems of Waring's type

2003 ◽  
Vol 92 (2) ◽  
pp. 181
Author(s):  
J Brüdern ◽  
K. Kawada ◽  
T. D. Wooley
Keyword(s):  
Additive Representation ◽  
Mixed Problems

scholarly journals Additive Representation in Thin Sequences, VII: Restricted Moments of the Number of Representations

2008 ◽  
Vol 32 (2) ◽  
pp. 383-406 ◽  
Author(s):  
Jörg Brüdern ◽  
Koichi Kawada ◽  
Trevor D. Wooley
Keyword(s):  
Additive Representation
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