For citation:
Matveev O. A. On a Particular Equivalent of Extended Riemann Hypothesis for Dirichlet L-functions on Numerical Fields. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 76-79. DOI: 10.18500/1816-9791-2013-13-4-76-79
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
25.11.2013
Full text:
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Language:
Russian
Heading:
UDC:
511.3
On a Particular Equivalent of Extended Riemann Hypothesis for Dirichlet L-functions on Numerical Fields
Autors:
Matveev Ol'ga Andreevna, Saratov State University
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
References:
- 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.
- 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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