All Questions

Update: The answer to the title question is no, as pointed out by Tapio and Willie. I would be more interested in lower bounds. Monsky's famous theorem with amazingly tricky proof says that if we ...

In the Boston conference on Fermat's Last Theorem (Summer 1995), Barry Mazur said (around 15m into the video) about class field theory that If you are a number-theorist and you want to cheer ...

I want to calculate the number of solutions to the quadratic equation $$x_1^2+\dots+x_m^2=0$$ where $m$ is odd (a given number) and $x_i\in\mathbb{Z}/p^n$ for a given prime number $p$ and a given ...

So rank $1$ local Langlands is special in as that it is given by the Artin map $$\text{GL}_1(K)\to G_K^{ab},$$ whereas in the higher rank (to the best of my knowledge) there doesn't exist a map $$\...