1. Generalized Limit Theorem for Mellin Transform of the Riemann Zeta-Function.
- Author
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Laurinčikas, Antanas and Šiaučiūnas, Darius
- Subjects
- *
MELLIN transform , *ZETA functions , *PROBABILITY measures , *DIFFERENTIABLE functions , *LIMIT theorems - Abstract
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 + i t , with fixed 1 / 2 < σ < 1 , of the square | ζ (1 / 2 + i t) | 2 of the Riemann zeta-function. We consider probability measures defined by means of Z (σ + i φ (t)) , where φ (t) , t ⩾ t 0 > 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 + i φ (t)) . This allows us to extend the distribution laws for Z (s) . [ABSTRACT FROM AUTHOR]
- Published
- 2024
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