Search Results

An update on this problem: I found out how to compute effective (and asymptotically accurate) bounds for $\sum_{p\leq x,\, p\equiv a\pmod{k}}\log(p)/p$. Basically it boils down to the usual analytic …

Let $f$ be a monotone decreasing, continuously differentiable function with $\lim_{x\rightarrow \infty}f(x)=0$. Let $\chi$ be a non-principal Dirichlet character. It is standard to show that $\sum_{ …

There are two main sources of repeated logs. (These sources can be further refined into natural subcategories, but I'll only mention a couple of those subcategories.) Those two main sources are: Typ …

The Riemann hypothesis is true, if primes are random in certain ways.

Suppose that $p$ is a prime number that divides $2^{2n+1}-1$. This means that $2^{2n+1}\equiv 1\pmod{p}$. Consequently, the order of $2$ modulo $p$ must be an odd number dividing $2n+1$. On the othe …

I think that there is indeed some possibility to lower the bound, and this is something I've looked at seriously a few times. I spent a semester (in 2019) with the Computational Number Theory Group h …