| Title:
|
The size of the Lerch zeta-function at places symmetric with respect to the line $\Re (s)=1/2$ (English) |
| Author:
|
Garunkštis, Ramūnas |
| Author:
|
Grigutis, Andrius |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
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69 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
25-37 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\zeta (s)$ be the Riemann zeta-function. If $t\geq 6.8$ and $\sigma >1/2$, then it is known that the inequality $|\zeta (1-s)|>|\zeta (s)|$ is valid except at the zeros of $\zeta (s)$. Here we investigate the Lerch zeta-function $L(\lambda ,\alpha ,s)$ which usually has many zeros off the critical line and it is expected that these zeros are asymmetrically distributed with respect to the critical line. However, for equal parameters $\lambda =\alpha $ it is still possible to obtain a certain version of the inequality $|L(\lambda ,\lambda ,1-\overline {s})|>|L(\lambda ,\lambda ,s)|$. (English) |
| Keyword:
|
Lerch zeta-function |
| Keyword:
|
functional equation |
| Keyword:
|
zero distribution |
| MSC:
|
11M35 |
| idZBL:
|
Zbl 07088766 |
| idMR:
|
MR3923571 |
| DOI:
|
10.21136/CMJ.2018.0149-17 |
| . |
| Date available:
|
2019-03-08T14:54:24Z |
| Last updated:
|
2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147614 |
| . |
| Reference:
|
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