Correlations of error terms for weighted prime counting functions

Shubhrajit Bhattacharya, Greg Martin, Reginald M. Simpson

Standard prime-number counting functions, such as $\ddot{I}ˆ(x)$, $\hat{I}¸(x)$, and $\ddot{I}€(x)$, have error terms with limiting logarithmic distributions once suitably normalized. The same is true…