| Title |
On generalized shifts of the Mellin transform of the Riemann zeta-function / |
| Authors |
Laurinčikas, Antanas ; Šiaučiūnas, Darius |
| DOI |
10.1515/math-2024-0055 |
| Full Text |
|
| Is Part of |
Open mathematics.. Warsaw : De Gruyter. 2024, vol. 22, iss. 1, art. no. 20240055, p. [1-15].. ISSN 2391-5455 |
| Keywords [eng] |
approximation of analytic functions ; limit theorem ; Mellin transform ; Riemann zeta-function ; weak convergence |
| Abstract [eng] |
In this article, we consider the asymptotic behavior of the modified Mellin transform Z(s), s=σ+it, of the Riemann zeta-function using weak convergence of probability measures in the space of analytic functions defined by means of shifts Z(s+iφ(τ)), where φ(τ) is a real increasing to +∞ differentiable function with monotonically decreasing derivative satisfying a certain estimate connected to the second moment of Z(s). We prove in this case that the limit measure is concentrated at the point g0(s)≡0. This result is applied to the approximation of g0(s) by shifts Z(s+iφ(τ)). |
| Published |
Warsaw : De Gruyter |
| Type |
Journal article |
| Language |
English |
| Publication date |
2024 |
| CC license |
|
