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VIDEO LIBRARY |
International Conference on Complex Analysis Dedicated to the Memory of Andrei Gonchar and Anatoliy Vitushkin
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Zeros and poles of the Helson zeta function I. A. Bochkov Saint Petersburg State University |
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Abstract: Let \begin{equation}\label{H} \zeta_\chi(s)=\sum_1^{\infty}\chi(n)n^{-s} . \end{equation} . The Riemann zeta function is thus a special case of the Helson zeta function. With this definition, $$ \zeta_\chi(s)=\prod_p\frac{1}{1-\chi(p)p^{-s}} . $$ In particular, Result of X. Helson (X . H. Helson, Compact groups and Dirichlet series, Ark. Mat. 8 (1969), 139–143.) asserts that for almost all Namely, for any potential sets of zeros and poles (without accumulation points, which is a necessary condition for an analytical function) in the band Website: https://zoom.us/j/98008001815?pwd=OG1rTVRFRzFpY3RhZmE4MXFwckxMUT09 * ID: 980 0800 1815; Password: 055016 |