Scholarly Publications - Mathematics

Permanent URI for this collectionhttps://hdl.handle.net/11693/115503

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Browsing Scholarly Publications - Mathematics by Author "Akbal, Yıldırım"

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    Friable values of piatetski-shapiro sequences
    (American Mathematical Society, 2017) Akbal, Yıldırım
    We give various estimates for friable values of Piatetski-Shapiro sequences.
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    On Waring-Goldbach problem with Piatetski-Shapiro primes
    (Academic Press, 2018) Akbal, Yıldırım; Güloğlu, Ahmet M.
    In this paper, we show that all sufficiently large natural numbers satisfying certain local conditions can be written as the sum of kth powers of Piatetski-Shapiro primes, thereby establishing a variant of Waring-Goldbach problem with primes from a sparse sequence.
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    Variations on a theme of Mirsky
    (World Scientific Publishing, 2022-07-05) Akbal, Yıldırım; Güloğlu, Ahmet
    Let k and r be non-zero integers with r≥2. An integer is called r-free if it is not divisible by the rth power of a prime. A result of Mirsky states that there are infinitely many primes p such that p+k is r-free. In this paper, we study an additive Goldbach-type problem and prove two uniform distribution results using these primes. We also study certain properties of primes p such that p+a1,…,p+aℓ are simultaneously r-free, where a1,…,aℓ are non-zero integers and ℓ≥1 .