| Title |
Discrete limit Bohr-Jessen type theorem for the Epstein zeta-function in short intervals |
| Authors |
LaurinΔikas, Antanas ; MacaitienΔ, Renata |
| DOI |
10.3390/axioms14080644 |
| Full Text |
|
| Is Part of |
Axioms.. Basel : MDPI. 2025, vol. 14, iss. 8, art. no. 644, p. [1-20].. eISSN 2075-1680 |
| Keywords [eng] |
Bohr-Jessen theorem ; Haar measure ; Epstein zeta-function ; convergence in distribution ; weak convergence of probability measures ; short intervals |
| Abstract [eng] |
We prove a probabilistic limit theorem for the Epstein zeta-function π(π ;π) in the interval [π,π+π] as πββ , using discrete shifts π(π+ππβ;π) , where β>0 and π>πβ12 are fixed. Here, Q is a positive-definite πΓπ matrix, and the interval length M satisfies ββ1(πβ)27/82β©½πβ©½ββ1(πβ)1/2 . The limit measure is given explicitly. This theorem is the first result in short intervals for π(π ;π) . The obtained theorem improves the known results established for the interval of length N. Since the considered probability measures are defined in terms of frequency, theorems in short intervals have a certain advantage in the detection of π(π+ππβ;π) with a given property, as well as in the characterization of the asymptotic behaviour of π(π ;π) in general. |
| Published |
Basel : MDPI |
| Type |
Journal article |
| Language |
English |
| Publication date |
2025 |
| CC license |
|
