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pro vyhledávání: '"Preobrazhenskii, Sergei"'
We consider a specific family of analytic functions $g_{\alpha,T}(s)$, satisfying certain functional equations and approximating to linear combinations of the Riemann zeta-function and its derivatives of the form $c_0\zeta(s)+c_1\frac{\zeta'(s)}{\log
Externí odkaz:
http://arxiv.org/abs/1805.07741
Autor:
Preobrazhenskii, Sergei
Feng and Wu introduced a new general coefficient sequence into Montgomery and Odlyzko's method for exhibiting irregularity in the gaps between consecutive zeros of $\zeta(s)$ assuming the Riemann Hypothesis. They used a special case of their sequence
Externí odkaz:
http://arxiv.org/abs/1505.05350
In this note we describe weight functions that exhibit a transitional behavior between weak and strong correlation with the Liouville function. We also describe a binary problem which may be considered as an interpolation between Chowla's conjecture
Externí odkaz:
http://arxiv.org/abs/1405.0682
Motivated by a functional property of the Riemann zeta function, we consider a new form of the mollified function in the Levinson-Conrey method. As an application, we give the following slight improvement of Feng's result: assuming Feng's condition o
Externí odkaz:
http://arxiv.org/abs/1403.5786
Autor:
Preobrazhenskii, Sergei
We prove an inversion formula for summatory arithmetic functions. As an application, we obtain an arithmetic relationship between summatory Piltz divisor functions and a sum of the M\"obius function over certain integers, denoted by $M(x,y)$. With th
Externí odkaz:
http://arxiv.org/abs/1301.4202
Autor:
Preobrazhenskii, Sergei
We prove an analogue of Selberg's explicit formula for Motohashi's product (see arXiv:1104.1358v3 [math.NT]). We also provide a zero-density theorem for the product, which follows from Soundararajan's theorem for moments of the Riemann zeta-function
Externí odkaz:
http://arxiv.org/abs/1105.0827
Autor:
Preobrazhenskii, Sergei
Assuming the Riemann hypothesis (RH) and using Littlewood's conditional estimates for the Riemann zeta-function, we provide an estimate related to an approach of Y. Motohashi to the zero-free region.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/1104.1358
Autor:
Preobrazhenskii, Sergei N.
It is shown that if a function defined on the segment [-1,1] has sufficiently good approximation by partial sums of the Legendre polynomial expansion, then, given the function's Fourier coefficients $c_n$ for some subset of $n\in[n_1,n_2]$, one may a
Externí odkaz:
http://arxiv.org/abs/1008.5035
Akademický článek
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Publikováno v:
Zhurnal nevropatologii i psikhiatrii imeni S.S. Korsakova (Moscow, Russia : 1952) [Zh Nevropatol Psikhiatr Im S S Korsakova] 1958; Vol. 58 (4), pp. 509-10.
