Sorry for such a direct question:

Consider the following integral:

$$I(t)=\int_{1/2}^{1} {\log|\zeta(a+it)|}da$$

How to find the nature of $I(t)$ as $t\rightarrow\infty$?

Sorry for such a direct question:

Consider the following integral:

$$I(t)=\int_{1/2}^{1} {\log|\zeta(a+it)|}da.$$

How to find the nature of $I(t)$ as $t\rightarrow\infty$?

Sorry for such a direct question:

Consider the following integral:

$$I(t)=\int_{1/2}^{1} {\log|\zeta(a+it)|}da$$

How to find the nature of $I(t)$ as $a\rightarrow\infty$?

Sorry for such a direct question:

Consider the following integral:

$$I(t)=\int_{1/2}^{1} {\log|\zeta(a+it)|}da$$

How to find the nature of $I(t)$ as $t\rightarrow\infty$?