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of 218
pro vyhledávání: '"Steuding, Jörn"'
We prove an effective universality theorem of the Riemann zeta-function in short intervals $[T,T+H]$ with $T^{\frac{27}{82}}\le H\le T$ by following an effective multidimensional $\Omega$-result of Voronin. Furthermore, we also prove the results in s
Externí odkaz:
http://arxiv.org/abs/2403.01787
Autor:
Andersson, Johan, Garunkštis, Ramūnas, Kačinskaitė, Roma, Nakai, Keita, Pańkowski, Łukasz, Sourmelidis, Athanasios, Steuding, Rasa, Steuding, Jörn, Wananiyakul, Saeree
We improve a recent universality theorem for the Riemann zeta-function in short intervals due to Antanas Laurin\v{c}ikas with respect to the length of these intervals. Moreover, we prove that the shifts can even have exponential growth. This research
Externí odkaz:
http://arxiv.org/abs/2312.04255
This article deals with applications of Voronin's universality theorem for the Riemann zeta-function $\zeta$. Among other results we prove that every plane smooth curve appears up to a small error in the curve generated by the values $\zeta(\sigma+it
Externí odkaz:
http://arxiv.org/abs/2306.00460
Publikováno v:
Number Theory in Memory of Eduard Wirsing (2023), H. Maier et al. (eds.), Springer Nature Switzerland AG, 307-321
We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the $a$-points of the zeta-function, i.e., the roots of the equation $\zeta(s)=a$, where $a$ is an arbitrary fixed complex number.
Externí odkaz:
http://arxiv.org/abs/2204.13887
We prove explicit bounds for the number of sums of consecutive prime squares below a given magnitude.
Externí odkaz:
http://arxiv.org/abs/2101.07558
Publikováno v:
Indag. Math. 33 Issue 6 (2022), 1236-1262
We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, for a fixed complex number $a\neq0$ and a function from the Selberg class $\mathcal{L}$, we prove a Riema
Externí odkaz:
http://arxiv.org/abs/2011.10692
Autor:
Steuding, Jörn, Suriajaya, Ade Irma
Publikováno v:
Comput. Methods Funct. Theory 20 (2020), no. 3-4, 389-401
For an arbitrary complex number $a\neq 0$ we consider the distribution of values of the Riemann zeta-function $\zeta$ at the $a$-points of the function $\Delta$ which appears in the functional equation $\zeta(s)=\Delta(s)\zeta(1-s)$. These $a$-points
Externí odkaz:
http://arxiv.org/abs/2007.14661
Publikováno v:
Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 2021, Vol. 314, pp. 248-274
The class of Dirichlet series associated with a periodic arithmetical function $f$ includes the Riemann zeta-function as well as Dirichlet $L$-functions to residue class characters. We study the value-distribution of these Dirichlet series $L(s;f)$,
Externí odkaz:
http://arxiv.org/abs/2007.14008