Greg Martin

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math.NT2025

Correlations of error terms for weighted prime counting functions

Shubhrajit Bhattacharya, Greg Martin, Reginald M. Simpson

Standard prime-number counting functions, such as $ψ (x)$ , $θ (x)$ , and $π (x)$ , have error terms with limiting logarithmic distributions once suitably normalized. The same is true of…

math.NT2025

The universal profile of the invariant factors of $(Z / n Z)^{\times}$

Greg Martin, Reginald M. Simpson

The structure of the multiplicative group $M_{n} = (Z / n Z)^{\times}$ encodes a great deal of arithmetic information about the integer $n$ (examples include $ϕ (n)$ , t…

Correlations of error terms for weighted prime counting functions

The universal profile of the invariant factors of (Z/nZ)×

The universal profile of the invariant factors of $(Z / n Z)^{\times}$