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VIDEO LIBRARY |
Conference to the Memory of Anatoly Alekseevitch Karatsuba on Number theory and Applications
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On the fractional [parts connecter with the function A. V. Shubin Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region |
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Abstract: The Dirichlet divisor problem is closely related to the sum of fractional parts $$ \sum_{n\le N}\left\{\frac{x}{n}\right\}\,=\,cN\,+\,O\bigl(x^{\alpha+\varepsilon}\bigr). $$ In the case In the talk, we will consider some asymptotic formulas for general sums $$ \sum_{\substack{n \le x \\ n \in \mathcal{A}}} f\left(\left\{\frac{x}{n}\right\}\right), \quad \sum_{n \le x}g(n)f\left(\left\{\frac{x}{n}\right\}\right), $$ where Language: Russian and English |