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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2015, Volume 15, Issue 1, Pages 37–45 (Mi isu562)  

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.

DOI: https://doi.org/10.18500/1816-9791-2015-15-1-37-45

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Bibliographic databases:

UDC: 511.3

Citation: V. A. Matveev, O. A. Matveeva, “Generalized characters over numerical fields and a counterpart of Chudakov hypothesis”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 15:1 (2015), 37–45

Citation in format AMSBIB
\Bibitem{MatMat15}
\by V.~A.~Matveev, O.~A.~Matveeva
\paper Generalized characters over numerical fields and a counterpart of Chudakov hypothesis
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2015
\vol 15
\issue 1
\pages 37--45
\mathnet{http://mi.mathnet.ru/isu562}
\crossref{https://doi.org/10.18500/1816-9791-2015-15-1-37-45}
\elib{http://elibrary.ru/item.asp?id=23144238}


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  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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