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Let      E ( T ) E(T)       denote the error term in the asymptotic formula for  \[    ∫  0 T | ζ  ( 1 2 + i t ) | 2 d t . \int _0^T {{{\left | {\zeta \left ( {\frac {1}{2} + it} \right )} \right |}^2}dt.}     \]  The function      E ( T ) E(T)       has mean value      π  \pi      . By      t n {t_n}       we denote the  n th zero of      E ( T ) −  π  E(T) - \pi      . Several results concerning      t n {t_n}       are obtained, including      t n + 1 −  t n ≪  t n 1 / 2 {t_{n + 1}} - {t_n} \ll t_n^{1/2}      . An algorithm is presented to compute the zeros of      E ( T ) −  π  E(T) - \pi       below a given bound. For      T ≤  5 T \leq 5      , 42010 zeros of      E ( T ) −  π  E(T) - \pi       were found. Various tables and figures are given, which present a selection of the computational results.

On the zeros of the error term for the mean square of |𝜁(\frac{1}2+𝑖𝑡)|