| Title |
On value distribution for the Mellin transform of the fourth power of the Riemann zeta function / |
| Authors |
Garbaliauskienė, Virginija ; Rimkevičienė, Audronė ; Stoncelis, Mindaugas ; Šiaučiūnas, Darius |
| DOI |
10.3390/axioms14010034 |
| Full Text |
|
| Is Part of |
Axioms.. Basel : MDPI. 2025, vol. 14, iss. 1, art. no. 34, p. [1-21].. eISSN 2075-1680 |
| Keywords [eng] |
limit theorem ; Mellin transform ; Riemann zeta function ; space of analytic functions ; weak convergence |
| Abstract [eng] |
In this paper, the asymptotic behavior of the modified Mellin transform 𝒵2(𝑠), 𝑠=𝜎+𝑖𝑡, of the fourth power of the Riemann zeta function is characterized by weak convergence of probability measures in the space of analytic functions. The main results are devoted to probability measures defined by generalized shifts 𝒵2(𝑠+𝑖𝜑(𝜏)) with a real increasing to +∞ differentiable functions connected to the growth of the second moment of 𝒵2(𝑠). It is proven that the mass of the limit measure is concentrated at the point expressed as ℎ(𝑠)≡0. This is used for approximation of ℎ(𝑠) by 𝒵2(𝑠+𝑖𝜑(𝜏)). |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2025 |
| CC license |
|
