Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Sourmelidis, Athanasios"'
We study lower bounds for the Riemann zeta function $\zeta(s)$ along vertical arithmetic progressions in the right-half of the critical strip. We show that the lower bounds obtained in the discrete case coincide, up to the constants in the exponentia
Externí odkaz:
http://arxiv.org/abs/2312.08011
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
Autor:
Sourmelidis, Athanasios
In 1975 Voronin proved the universality theorem for the Riemann zeta-function $\zeta(s)$ which roughly says that any admissible function $f(s)$ is approximated by $\zeta(s)$. A few years later Reich proved a discrete analogue of this result. The proo
Externí odkaz:
http://arxiv.org/abs/2308.07031
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
We investigate the averages of Dedekind sums over rational numbers in the set $$\mathscr{F}_\alpha(Q):=\{\, {v}/{w}\in \mathbb{Q}: 0
Externí odkaz:
http://arxiv.org/abs/2301.00441
Publikováno v:
Math. Ann. 387, 291--320 (2023)
We investigate the number of steps taken by three variants of the Euclidean algorithm on average over Farey fractions. We show asymptotic formulae for these averages restricted to the interval $(0,1/2)$, establishing that they behave differently on $
Externí odkaz:
http://arxiv.org/abs/2206.03214
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
Autor:
Sourmelidis, Athanasios
The starting point of the thesis is the {\it universality} property of the Riemann Zeta-function $\zeta(s)$ which was proved by Voronin in 1975: {\it Given a positive number $\varepsilon>0$ and an analytic non-vanishing function $f$ defined on a comp
Fix $\alpha,\theta >0$, and consider the sequence $(\alpha n^{\theta} \mod 1)_{n\ge 1}$. Since the seminal work of Rudnick--Sarnak (1998), and due to the Berry--Tabor conjecture in quantum chaos, the fine-scale properties of these dilated mononomial
Externí odkaz:
http://arxiv.org/abs/2106.09800
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