On Value Distribution for the Mellin Transform of the Fourth Power of the Riemann Zeta Function

被引：0

作者：

Garbaliauskiene, Virginija ^{[1
]}

Rimkeviciene, Audrone ^{[2
]}

Stoncelis, Mindaugas ^{[1
]}

Siauciunas, Darius ^{[1
]}

机构：

[1] Vilnius Univ, Inst Reg Dev, Siauliai Acad, P Visinskio Str 25, LT-76351 Shiauliai, Lithuania

[2] Siauliu Valstybine Kolegija, Fac Business & Technol, Ausros Av 40, LT-76241 Shiauliai, Lithuania

来源：

AXIOMS | 2025年 / 14卷 / 01期

关键词：

limit theorem; Mellin transform; Riemann zeta function; space of analytic functions; weak convergence; ANALYTIC-FUNCTIONS; LIMIT-THEOREMS; UNIVERSALITY; SQUARE;

D O I：

10.3390/axioms14010034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the asymptotic behavior of the modified Mellin transform Z2(s), s=sigma+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+i phi(tau)) with a real increasing to +infinity 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)equivalent to 0. This is used for approximation of h(s) by Z2(s+i phi(tau)).

引用

页数：21