| Title |
On shifts of periodic zeta-function in short intervals |
| Authors |
Grigaliūnas, Marius ; Laurinčikas, Antanas ; Šiaučiūnas, Darius |
| DOI |
10.3846/mma.2026.24070 |
| Full Text |
|
| Is Part of |
Mathematical modelling and analysis.. Vilnius : Vilnius Gediminas Technical University. 2026, vol. 31, iss. 1, p. 63-78.. ISSN 1392-6292. eISSN 1648-3510 |
| Keywords [eng] |
approximation of analytic functions ; Dirichlet series ; Hurwitz zeta-function ; periodic zeta-function ; weak convergence |
| Abstract [eng] |
The periodic zeta-function ζ(s; a), s = σ + it, a = {am ∈C : m ∈ N}, in the half-plane σ > 1 is defined by Dirichlet series with periodic coefficients am, and has the meromorphic continuation to the whole complex plane. The function ζ(s; a) is a generalization of the Riemann zeta-function and Dirichlet L-functions. In the paper, using only the periodicity of the sequence a, we obtain that the shifts ζ(s + iτ; a), τ ∈ R, approximate a certain class of analytic functions, defined in the strip {s ∈ C : 1/2 < σ < 1}. For T 23/70 ⩽ H ⩽ T 1/2, the set of such shifts has a positive lower density in the interval [T, T + H], T → ∞. The case of positive density is also discussed. For the proof, the mean square estimate in short intervals for the Hurwitz zeta-function, and probabilistic limit theorems are applied. |
| Published |
Vilnius : Vilnius Gediminas Technical University |
| Type |
Journal article |
| Language |
English |
| Publication date |
2026 |
| CC license |
|
