Geodesic
Generalized characters over numerical fields and a counterpart of Chudakov hypothesis
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 1, pp. 37-45.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ISU_2015_15_1_a5,
     author = {V. A. Matveev and O. A. Matveeva},
     title = {Generalized characters over numerical fields and a counterpart of {Chudakov} hypothesis},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {37--45},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2015_15_1_a5/}
}
TY  - JOUR
AU  - V. A. Matveev
AU  - O. A. Matveeva
TI  - Generalized characters over numerical fields and a counterpart of Chudakov hypothesis
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2015
SP  - 37
EP  - 45
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ISU_2015_15_1_a5/
LA  - ru
ID  - ISU_2015_15_1_a5
ER  - 
%0 Journal Article
%A V. A. Matveev
%A O. A. Matveeva
%T Generalized characters over numerical fields and a counterpart of Chudakov hypothesis
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2015
%P 37-45
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ISU_2015_15_1_a5/
%G ru
%F ISU_2015_15_1_a5
V. A. Matveev; O. A. Matveeva. Generalized characters over numerical fields and a counterpart of Chudakov hypothesis. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 1, pp. 37-45. http://geodesic.mathdoc.fr/item/ISU_2015_15_1_a5/

[1] Kheil'bronn H., “$\zeta$-functions and $L$-functions”, Algebraic Number Theory, Mir, M., 1968, 310–346 (in Russian)

[2] Chudakov N. G., Linnik J. A., “On certain class of completely multiplicative functions”, USSR AS Reports, 74:2 (1950), 193–196 (in Russian)

[3] Chudakov N. G., Rodosskii K. A., “On generalized character”, USSR AS Reports, 74:3 (1950), 1137–1138 (in Russian)

[4] Glazkov V. V., “Characters of multiplicative semigroup of natural numbers”, Interacademic tractate collection, Number theory research, 2, Saratov Univ. Press, Saratov, 1968, 3–40 (in Russian)

[5] Kuznetsov V. N., Setsinskaia E. V., Krivobok V. V., “On a problem of decomposition into a product of Dirichlet $L$-functions over numerical fields”, Chebyshev collection, 5:3 (2004), 51–64 (in Russian)

[6] Vodolazov A. M., Kuznetsov V. N., “On analytical continuation of Dirichlet series with multiplicative coefficients”, Interacademic tractate collection, Research on algebra, number theory and complementary areas, 1, Saratov Univ. Press, Saratov, 2003, 43–59 (in Russian)

[7] Dem'ianov V. F., Malozemov V. N., Introduction to minimax, Nauka, M., 1982, 368 pp. (in Russian)

[8] Postnikov A. G., Introduction to analytical number theory, Nauka, M., 1971, 416 pp. (in Russian)