| Title |
Generalized limit theorem for Mellin transform of the Riemann zeta-function |
| Authors |
Laurinčikas, Antanas ; Šiaučiūnas, Darius |
| DOI |
10.3390/axioms13040251 |
| Full Text |
|
| Is Part of |
Axioms.. Basel : MDPI. 2024, vol. 13, iss. 4, art. no. 251, p. [1-17].. ISSN 2075-1680 |
| Keywords [eng] |
modified Mellin transform ; Riemann zeta-function ; weak convergence of probability measures |
| Abstract [eng] |
In the paper, we prove a limit theorem in the sense of the weak convergence of probability measures for the modified Mellin transform Z(s), s = σ + it, with fixed 1/2 < σ < 1, of the square |ζ(1/2 + it)| 2 of the Riemann zeta-function. We consider probability measures defined by means of Z(σ + iφ(t)), where φ(t), t ⩾ t0 > 0, is an increasing to +∞ differentiable function with monotonically decreasing derivative φ′(t) satisfying a certain normalizing estimate related to the mean square of the function Z(σ + iφ(t)). This allows us to extend the distribution laws for Z(s). |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2024 |
| CC license |
|
