Перегляд за Автор "Shramko, Valeriia V."

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    Gaussian integers partition in power-free numbers product
    (Одеський національний університет імені І. І. Мечникова, 2020) Shramko, Valeriia V.; Шрамко, Валерія Вадимівна; Шрамко, Валерия Вадимовна
    Let g1(𝛼) be the number of Gaussian integer 𝛼 representation in a product of square-free factors. Let g2(𝛼) be the number of Gaussian integer 𝛼 representation in a product of power-free factors. In this paper we consider their summatory functions Σ︀𝑁(𝛼)≤𝑥 g1(𝛼) andΣ︀𝑁(𝛼)≤𝑥 g2(𝛼) and obtain asymptotic formulas for them. Also, we prove analogue of K´atai- Subbarao theorem to study the distribution of g2(𝛼) in increasing norm order case.