Consider the following integral:


Where , $$f(x)=\sin^2(πx)+\sin^2(π(1+\Gamma(x))/x)$$

The integral extends over a closed contour $C_n$ enclosing a segment $x$- axis from $1$ to $n$ and narrow enough to contain no complex zero.

We can clearly see that $f(x)$ has real zeroes only at primes .

This integral is considered by S.Wigert.

Question: Is this analysis "resurrectable"? By resurrectable I mean can this be modified such that it may be workable?

  • 2
    $\begingroup$ "workable" for what purpose. No target, goal, path, or intent is specified. $\endgroup$ Mar 16, 2020 at 18:53
  • $\begingroup$ @EricTowers to get an estimate on $π(n)$. $\endgroup$
    – bambi
    Mar 16, 2020 at 19:02


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