Background: In the 1700s, Euler solved the Basel Problem, which was to solve $\sum_{n=1}^\infty\frac{1}{n^2}$ in closed-form. Euler showed that it was equal to $\frac{\pi^2}{6}$ b …

In Theorem 3.2 of 'Introduction to spectral theory of automorphic forms' by Iwaniec,the first bound is about the coefficients of automorphic forms $$\sum_{|n|\le N}|n||c_n|^2<& …

greetings . i've been trying to do this integral for many days now, with no clue on how to attack it . the integral is a mellin inverse of some kind, and appears in analytic number …

Can anyone give an estimate (upper bound or lower bound) for the number of divisors $d\mid P_r$ such that $\frac{\sqrt{P_r}}{2}< d < \sqrt{P_r}$, where $P_r$ is the product o …

Hi there, Can we say that if $p$ and $q$ are distinct prime number diving $n$ $\Omega(gcd(p-1,q-1)) \leq \Omega(n)$ Where $\Omega(n)$ denotes the number of prime powers dividing …

We know that by Dirichlet's formula for the Divisor function $ \displaystyle \sum\limits_{n \leq x} d(n) = x \log{x} + (2C-1)x + \mathcal{O}(\sqrt{x})$. What is the best approxim …