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( I've been thinking about asking this for a long time . Though this is not rigorous; It can be thought of as heuristic or extraction of information from different viewpoint.) We know "super-...

Consider the analytic function $g(x)$ Define $$f(x)=g(x)\frac{\sin^2\left(\frac{π\Gamma(x)}{2x}\right)}{\cos^2\left(\frac{π}{2x}\right)}$$ Note that: $$f(p)=g(p) \text{ for prime } p$$ And $f(n)=0$ ...

Consider the following function : $$F(z) = \omega(z){\sin^2\left(\frac{c\Gamma(z)}{z}\right)}$$ Here, $\omega(z)$ is a weight we are going to consider The following two conditions should meet for $\...

Consider the analytic function $g(x)$ Now define $f(x)=g(x)\frac{\sin^2\left(\frac{π\Gamma(x)}{2x}\right)}{\cos^2\left(\frac{π}{2x}\right)}$ Such that $|f(x+it)|=o(e^{2πt})$ uniformly for every $x$...