On a version of Hadamard’s method in the theory of Dirichlet’s L-functions
https://doi.org/10.22405/2226-8383-2019-20-3-
Abstract
In the paper a new version of the Hadamard’s method in the theory of Dirichlet’s L-functions
is given. We prove of this method of the absence of the L-functions zeroes on the unit line. We
show that the Hadamard’s method allow to get results, which on the accuracy correspond to the
Vallee Poussin results in the asymptotical law of the distribution of primes. Of this we extend
possibilities of the Hadamard’s method. New estimations of the zeta-sum twisted together with
the Dirichlet’s character by modulo, equals to the degree of an odd prime number are obtained
that permits to get the modern limit of zeroes for the corresponding Dirichlet’s L-function.
About the Authors
Olga Viktorovna KolpakovaRussian Federation
O. V. Popov
Russian Federation
Vladimir Nikolaevich Chubarikov
Russian Federation
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Review
For citations:
Kolpakova O.V., Popov O.V., Chubarikov V.N. On a version of Hadamard’s method in the theory of Dirichlet’s L-functions. Chebyshevskii Sbornik. 2019;20(3):282-295. (In Russ.) https://doi.org/10.22405/2226-8383-2019-20-3-
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