Geodesic
The size of the Lerch zeta-function at places symmetric with respect to the line $\Re (s)=1/2$
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 25-37 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $|L(\lambda ,\lambda ,1-\overline {s})|>|L(\lambda ,\lambda ,s)|$.
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 $|L(\lambda ,\lambda ,1-\overline {s})|>|L(\lambda ,\lambda ,s)|$.
DOI : 10.21136/CMJ.2018.0149-17
Classification : 11M35
Keywords: Lerch zeta-function; functional equation; zero distribution 
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     title = {The size of the {Lerch} zeta-function at places symmetric with respect to the line $\Re (s)=1/2$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {25--37},
     year = {2019},
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Garunkštis, Ramūnas; Grigutis, Andrius. The size of the Lerch zeta-function at places symmetric with respect to the line $\Re (s)=1/2$. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 25-37. doi: 10.21136/CMJ.2018.0149-17

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