| Title |
A joint limit theorem for Epstein and Hurwitz zeta-functions |
| Authors |
Gerges, Hany ; Laurinčikas, Antanas ; Macaitienė, Renata |
| DOI |
10.3390/math12131922 |
| Full Text |
|
| Is Part of |
Mathematics.. Basel : MDPI. 2024, vol. 12, iss. 13, art. no. 1922, p. [1-15].. ISSN 2227-7390 |
| Keywords [eng] |
Dirichlet L-function ; Epstein zeta-function ; Hurwitz zeta-function ; limit theorem ; Haar probability measure ; weak convergence |
| Abstract [eng] |
In the paper, we prove a joint limit theorem in terms of the weak convergence of probability measures on C^2 defined by means of the Epstein ζ(s;Q) and Hurwitz ζ(s,α) zeta-functions. The limit measure in the theorem is explicitly given. For this, some restrictions on the matrix Q and the parameter α are required. The theorem obtained extends and generalizes the Bohr-Jessen results characterising the asymptotic behaviour of the Riemann zeta-function. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2024 |
| CC license |
|
