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On the monotonicity properties of additive representation functions

Published online by Cambridge University Press:  17 April 2009

Yong-Gao Chen ,
András Sárközy ,
Vera T. Sós  and
Min Tang
Yong-Gao Chen
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, China
András Sárközy
Affiliation:
Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary
Vera T. Sós
Affiliation:
Department of Algebra and Number Theory, Eötvös Loránd University, H-1117 Budapest, Pázmány Péter sétány 1/c, Hungary
Min Tang
Affiliation:
Department of Mathematics, Anhui Normal University, Wuhu 241000, China
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If A is a set of positive integers, let R1 (n) be the number of solutions of a + a′ = n, a. a′ ∈ A, and let R2(n) and R3(n) denote the number of solutions with the additional restrictions a < a′, and a ≤ a′ respectively. The monotonicity properties of the three functions R1(n), R2(n), and R3(n) are studied and compared.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 72 , Issue 1 , August 2005 , pp. 129 - 138
Copyright
Copyright © Australian Mathematical Society 2005

References

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