All Questions

In their paper "Moyenne de certains fonctions arithmétiques sur les entiers friables", Tenenbaum and Wu proved that for the case of the function $\beta$ which is the indicator function of ...

I am currently working on some tools to make contour integration in a proof assistant less painful and I'm looking for interesting examples of contours in the complex plane used in the literature. I ...

Sorry for such a direct question: Consider the following integral: $$I(t)=\int_{1/2}^{1} {\log|\zeta(a+it)|}da.$$ How to find the nature of $I(t)$ as $t\rightarrow\infty$?

I am teaching a graduate course in Complex Analysis and I am covering Newman's proof of the prime number theorem. I have been using the simplified version in the papers of Zagier and Korevaar. However,...

Consider the following function: $$F(z) = \omega(z)\sin^2\left(\frac{c\Gamma(z)}{z}\right)$$ Here, $\omega(z)$ is a weight we have to construct and $c$ is a constant. The following three conditions ...