| Autor: |
Zhenjiang Pan, Zhengang Wu |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
AIMS Mathematics, Vol 9, Iss 6, Pp 16564-16585 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.2024803?viewType=HTML |
| Popis: |
In this paper, we derive the asymptotic formulas $ B^*_{r, s, t}(n) $ such that $ \mathop{\lim} \limits_{n \rightarrow \infty} \left\{ \left( \sum\limits^{\infty}_{k = n} \frac{1}{k^r(k+t)^s} \right)^{-1} - B^*_{r,s,t}(n) \right\} = 0, $ where $ Re(r+s) > 1 $ and $ t \in \mathbb{C} $. It is evident that the asymptotic formulas for the inverses of the tails of both the Riemann zeta function and the Hurwitz zeta function on the half-plane $ Re(s) > 1 $ are its corollaries. Subsequently we provide the asymptotic formulas for the Riemann zeta function and the Hurwitz zeta function on the half-plane $ Re(s) < 0 $. Finally, we study the asymptotic formulas of the inverse of the tails of the Dirichlet L-function for $ Re(s) > 1 $ and $ Re(s) < 0 $. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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