| Title |
The discrete value distribution of the modified Mellin transform of the fourth power of the Riemann zeta-function |
| Authors |
Garbaliauskienė, Virginija ; Macaitienė, Renata ; Rimkevičienė, Audronė ; Stoncelis, Mindaugas ; Šiaučiūnas, Darius |
| DOI |
10.3390/axioms15040293 |
| Full Text |
|
| Is Part of |
Axioms.. Basel : MDPI. 2026, vol. 15, iss. 4, art. no. 293, p. [1-19].. eISSN 2075-1680 |
| Keywords [eng] |
Mellin transform ; probability measure ; Riemann zeta-function ; space of analytic functions ; weak convergence |
| Abstract [eng] |
Abstract Let 𝒵2(𝑠) denote the modified Mellin transforms of the modulus of the fourth power of the Riemann zeta-function. This paper is devoted to the probabilistic properties of generalized discrete shifts 𝒵2(𝑠+𝑖𝜓(𝑘)), 𝑘∈ℕ, with a certain differentiable function 𝜓(𝜏) satisfying some estimate connected to the mean square of the function 𝒵2(𝑠) and such that the sequence {𝜅𝜓(𝑘):𝑘∈ℕ} is uniformly distributed modulo 1 with every 𝜅∈ℝ∖{0}. We propose the condition that 𝒵2(𝑠+𝑖𝜓(𝑘)) in the space of analytic functions has a limit distribution concentrated at the point 𝑔0(𝑠)≡0. Such a limit theorem is applied for the approximation of the function 𝑔0(𝑠) . |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2026 |
| CC license |
|
