A generalization of a theorem of Erdős-Rényi to m-fold sums and differences

• Autorzy: Kathryn E. Hare , Shuntaro Yamagishi
• Języki publikacji: EN

Abstrakty

EN

Let m ≥ 2 be a positive integer. Given a set E(ω) ⊆ ℕ we define $r_{N}^{(m)}(ω)$ to be the number of ways to represent N ∈ ℤ as a combination of sums and differences of m distinct elements of E(ω). In this paper, we prove the existence of a "thick" set E(ω) and a positive constant K such that $r_{N}^{(m)}(ω) < K$ for all N ∈ ℤ. This is a generalization of a known theorem by Erdős and Rényi. We also apply our results to harmonic analysis, where we prove the existence of certain thin sets.

Kategorie tematyczne

• 11B83: Special sequences and polynomials
• 11K31: Special sequences
• 43A46: Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 166
• Numer: 1
• Strony: 55-67

Daty

wydano

2014

Twórcy

autor

Kathryn E. Hare

• Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1

autor

Shuntaro Yamagishi

• Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1

Identyfikatory

DOI

10.4064/aa166-1-5