A Joint Limit Theorem for Epstein and Hurwitz Zeta-Functions

Hany Gerges, Antanas Laurinčikas and Renata Macaitienė ()
Additional contact information
Hany Gerges: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania
Antanas Laurinčikas: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania
Renata Macaitienė: Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania

Mathematics, 2024, vol. 12, issue 13, 1-15

Abstract: 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.

Keywords: Dirichlet L-function; Epstein zeta-function; Hurwitz zeta-function; limit theorem; Haar probability measure; weak convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/13/1922/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/13/1922/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:13:p:1922-:d:1419404

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().