Zobrazeno 1 - 10
of 63
pro vyhledávání: '"Darius Šiaučiūnas"'
Publikováno v:
Mathematical Modelling and Analysis, Vol 29, Iss 2 (2024)
The Lerch zeta-function depends on two real parameters λ and and, for σ > 1, is defined by the Dirichlet series , and by analytic continuation elsewhere. In the paper, we consider the joint approximation of collections of analytic functions by disc
Externí odkaz:
https://doaj.org/article/fdd97c8970c3413790f98a86321478de
Autor:
Antanas Laurinčikas, Darius Šiaučiūnas
Publikováno v:
Axioms, Vol 13, Iss 8, p 510 (2024)
The Hurwitz zeta-function ζ(s,α), s=σ+it, with parameter 0<α⩽1 is a generalization of the Riemann zeta-function ζ(s) (ζ(s,1)=ζ(s)) and was introduced at the end of the 19th century. The function ζ(s,α) plays an important role in investigat
Externí odkaz:
https://doaj.org/article/efd1319b66f949478df3ab7c87f32c32
Autor:
Antanas Laurinčikas, Darius Šiaučiūnas
Publikováno v:
Axioms, Vol 13, Iss 4, p 251 (2024)
In the paper, we prove a limit theorem in the sense of the weak convergence of probability measures for the modified Mellin transform Z(s), s=σ+it, with fixed 1/2<σ<1, of the square |ζ(1/2+it)|2 of the Riemann zeta-function. We consider probabilit
Externí odkaz:
https://doaj.org/article/ac7c5c47747f4ace8247877b66f7d331
Publikováno v:
Mathematical Modelling and Analysis, Vol 28, Iss 2 (2023)
In 1973, Voronin proved the functional independence of the Riemann zeta-function ζ(s), i.e., that ζ(s) and its derivatives do not satisfy a certain equation with continuous functions. In the paper, we obtain a joint version of the Voronin theorem.
Externí odkaz:
https://doaj.org/article/7ddced36c5a8422e971bfcc5ec7407bb
Autor:
Darius Šiaučiūnas, Monika Tekorė
Publikováno v:
Mathematics, Vol 11, Iss 22, p 4615 (2023)
Let a={am:m∈N} be a periodic multiplicative sequence of complex numbers and L(s;a), s=σ+it a Dirichlet series with coefficients am. In the paper, we obtain a theorem on the approximation of non-vanishing analytic functions defined in the strip 1/2
Externí odkaz:
https://doaj.org/article/0cf292440997482688978c5968423ac6
Publikováno v:
Mathematics, Vol 11, Iss 10, p 2315 (2023)
In the paper, it is obtained that there are infinite discrete shifts Ξ(s+ikh), h>0, k∈N0 of the Mellin transform Ξ(s) of the square of the Riemann zeta-function, approximating a certain class of analytic functions. For the proof, a probabilistic
Externí odkaz:
https://doaj.org/article/1a72fafd14554a30bfff83a687fc962c
Publikováno v:
Mathematics, Vol 11, Iss 9, p 2042 (2023)
Let a={am} and b={bm} be two periodic sequences of complex numbers, and, additionally, a is multiplicative. In this paper, the joint approximation of a pair of analytic functions by shifts (ζnT(s+iτ;a),ζnT(s+iτ,α;b)) of absolutely convergent Dir
Externí odkaz:
https://doaj.org/article/4aa6440c16824616980c7223331ee76d
Publikováno v:
Mathematical Modelling and Analysis, Vol 26, Iss 1, Pp 21-33 (2021)
In 2007, H. Mishou obtained a joint universality theorem for the Riemann and Hurwitz zeta-functions ζ(s) and ζ(s,α) with transcendental parameter α on the approximation of a pair of analytic functions by shifts (ζ(s+iτ),ζ(s+iτ,α)), τ ∈R.
Externí odkaz:
https://doaj.org/article/d1fdb0b7987d4e9f808f722c1f4d7aa5
Publikováno v:
Mathematical Modelling and Analysis, Vol 27, Iss 1, Pp 78–87-78–87 (2022)
In the paper, an universality theorem of discrete type on the approximation of analytic functions by shifts of a special absolutely convergent Dirichlet series is obtained. These series is close in a certain sense to the periodic zeta-function and de
Externí odkaz:
https://doaj.org/article/6bdd1059751b4be29cc17d78fbf20151
Publikováno v:
Mathematics, Vol 11, Iss 3, p 752 (2023)
In this paper, we consider the simultaneous approximation of tuples of analytic functions by tuples of shifts of Lerch zeta-functions with arbitrary parameters. We prove that there exists a closed set of tuples of functions analytic in the right-hand
Externí odkaz:
https://doaj.org/article/3339c0551be2444abdb1a9fe54ac3bae