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- Title
Additive representation functions and discrete convolutions.
- Authors
Sándor, Cs.
- Abstract
For a set A of non-negative integers, let RA(n) denote the number of solutions to the equation n = a + a ′ with a, a ′ ∈ A . Denote by χ A (n) the characteristic function of A. Let b n > 0 be a sequence satisfying limsup n → ∞ b n < 1 . In this paper, we prove some Erdős–Fuchs-type theorems about the error terms appearing in the approximation formulæ for R A (n) = ∑ k = 0 n χ A (k) χ A (n - k) and ∑ n = 0 N R A (n) having principal terms ∑ k = 0 n b k b n - k and ∑ n = 0 N ∑ k = 0 n b k b n - k , respectively.
- Subjects
ADDITIVE functions; CHARACTERISTIC functions; INTEGERS
- Publication
Acta Mathematica Hungarica, 2022, Vol 166, Issue 2, p217
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1007/s10474-022-01225-2