In this paper we establish, by elementary means, estimates for the sum of
some functions in certain arithmetic progressions.Comment: typos correcte

Agama, Theophilus

English

arXiv

In this paper we introduce a multivariate version of circles of partition
introduced and studied in \cite{CoP}. As an application we prove a weaker
general version of the Erd\H{o}s-Tur\'{a}n additive base conjecture. The actual
Erd\H{o}s-Tur\'{a}n additive base conjecture follows from this general version
as a consequence.Comment: The authors of this recent submission had a lot of trouble trying to
  salvage a crucial Lemma needed to make the elementary proof of Lemoine's
  conjecture work. After spates of vain attempts the first author has now
  decided to upload a more general proof of the Erdos-Turan additive base
  conjecture as a replacemen

On elementary estimates for sum of some functions in certain arithmetic progressions

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