Cite this article as:

Matveev O. A., Matveev V. A. On a Particular Equivalent of Extended Riemann Hypothesis for Dirichlet L-functions on Numerical Fields. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2013, vol. 13, iss. 4, pp. 76-79. DOI: https://doi.org/10.18500/1816-9791-2013-13-4-76-79

Language: 
Russian
Heading: 
Mathematics
UDC: 
511.3

On a Particular Equivalent of Extended Riemann Hypothesis for Dirichlet L-functions on Numerical Fields

Authors: 
Matveev Ol'ga Andreevna, Saratov State University, Russia, Saratov, Astrakhanskaya 83 , olga.matveeva.0@gmail.com
Matveev Vladimir Alekseyevich , Saratov State University, Russia, Saratov, Astrakhanskaya 83 , vladimir.matweev@gmail.com
Abstract: 
A condition on summatory function over a set of prime ideals for Dirichlet L-functions on numerical fields is obtained. This condition is equivalent to extended Riemann hypothesis. Analytical properties of Euler products associated with this equivalent are studied
Key words: 
extended Riemann hypothesis, Dirichlet L-functions, numerical fields.
DOI: 
https://doi.org/10.18500/1816-9791-2013-13-4-76-79
References
1. Hardy G. H., Littlewood J. E. Some problems of partitio numerorum III : On the expression of a number as a sum of primes. Acta Mathematica, 19232, vol. 44, pp. 1–70.
2. Kheil’bronn Kh. ³-funktsii i L-funktsii [³-functions and L-functions]. Algebraicheskaia teoriia chisel [Algebraic number theory], Moscow, Mir, 1969, pp. 310–346 (in Russian)
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