Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Author: search.filters.author.Sertbaş, Doğa CanCOAR Access Rights: search.filters.coarAccessRights.metadata only access

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  • Article
    On Classification of Sequences Containing Arbitrarily Long Arithmetic Progressions
    (World Scientific Publishing, 2023) Cam Çelik, Şermin; Eyidoğan, Sadık; Göral, Haydar; Sertbaş, Doğa Can
    In this paper, we study the classification of sequences containing arbitrarily long arithmetic progressions. First, we deal with the question how the polynomial map n(s) can be extended so that it contains arbitrarily long arithmetic progressions. Under some growth conditions, we construct sequences which contain arbitrarily long arithmetic progressions. Also, we give a uniform and explicit arithmetic progression rank bound for a large class of sequences. Consequently, a dichotomy result is deduced on the finiteness of the arithmetic progression rank of certain sequences. Therefore, in this paper, we see a way to determine the finiteness of the arithmetic progression rank of various sequences satisfying some growth conditions.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Applications of Class Numbers and Bernoulli Numbers To Harmonic Type Sums
    (Korean Mathematical Society, 2021) Göral, Haydar; Sertbaş, Doğa Can
    Divisibility properties of harmonic numbers by a prime number p have been a recurrent topic. However, finding the exact p-adic orders of them is not easy. Using class numbers of number fields and Bernoulli numbers, we compute the exact p-adic orders of harmonic type sums. Moreover, we obtain an asymptotic formula for generalized harmonic numbers whose p-adic orders are exactly one.