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## Tagged Questions

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### Can infinite polynomials be expressed as a product of its linear factors?

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 …
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### About Theorem 3.2 in ‘introduction to spectral theory of automorphic forms’ by Iwaniec

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<& …
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### Help with a mellin-type integral

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 …
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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 …