R. Romanov

activity

20152021

collaborators

3 papers

math.NT2021

On zeroes and poles of Helson zeta functions

I. Bochkov, R. Romanov

We show that the analytic continuations of Helson zeta functions $ζ_{χ} (s) = \sum_{1}^{\infty} χ (n) n^{- s}$ can have essentially arbitrary poles and zeroes in the strip $ 21/40 < \Re s…

math.SP2019

Canonical systems with discrete spectrum

Roman Romanov, Harald Woracek

We study spectral properties of two-dimensional canonical systems $y^{'} (t) = z J H (t) y (t)$ , $t \in [a, b)$ , where the Hamiltonian $H$ is locally integrable on $[a, b)$ , positive semidefinite…

math.SP2015

Order problem for canonical systems and a conjecture of Valent

Roman Romanov

We establish a sharp upper estimate for the order of a canonical system in terms of the Hamiltonian. This upper estimate becomes an equality in the case of Krein strings. As an app…