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VIDEO LIBRARY |
International conference on Analytic Number Theory dedicated to 75th anniversary of G. I. Arkhipov and S. M. Voronin
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On a special trigonometric series and its applications, as well as the memories K. I. Oskolkov University of South Carolina, Columbia, SC |
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Abstract: The talk is devoted to the common results of the speaker and G.I. Arkhipov concerning the behavior of the series of the type $$ h(P)\,=\,\sum\limits_{n\ne 0}\frac{e^{2\pi iP(n)}}{n}, $$ and of their symmetric partial sums $$ h_{N}(P)\,=\,\sum\limits_{1\leqslant |n|\leqslant N}\frac{e^{2\pi iP(n)}}{n}, $$ where $$ P(x)\,=\,P(x;\boldsymbol{\alpha})\,=\,\alpha_{1}x+\alpha_{2}x^{2}\,+\ldots\,+\alpha_{r}x^{r} $$ is a polynomial of degree |