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Mathematics
Generalized characters over numerical fields and a counterpart of Chudakov hypothesis
V. A. Matveev, O. A. Matveeva Saratov State University, 83, Astrakhanskaya str., 410012, Saratov, Russia
Abstract:
The well-known Chudakov hypothesis for numeric characters, conjectured by Chudakov in 1950, suggests that finite-valued numeric character $h(n)$, which satisfies the following conditions: 1) $h(p) \neq 0$ for almost all prime $p$; 2) $S(x) = \sum\limits_{n \leq x} h(n) = \alpha x + O(1)$, is a Dirichlet character. A numeric character which satisfies these conditions is called a generalized character, principal if $\alpha \neq 0$ and non-principal otherwise. Chudakov hypothesis for principal characters was proven in 1964, but for non-principal ones thus far it remains unproved. In this paper we present a definition of generalized character over numerical fields, suggest an analog of Chudakov hypothesis for these characters and provide its proof for principal generalized characters.
Key words:
Chudakov hypothesis, generalized numerical characters.
Citation:
V. A. Matveev, O. A. Matveeva, “Generalized characters over numerical fields and a counterpart of Chudakov hypothesis”, Izv. Saratov Univ. Math. Mech. Inform., 15:1 (2015), 37–45
Linking options:
https://www.mathnet.ru/eng/isu562 https://www.mathnet.ru/eng/isu/v15/i1/p37
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Abstract page: | 199 | Full-text PDF : | 92 | References: | 48 |
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