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I really like the exposition in these notes of Soundararajan (start on page 18). His proof is conditional on GRH, which strips the method down to a very easily understood core. I think it would be ext …

Can anyone please recommend some good reading on the geometry of linear groups and their actions? An example of the kind of question I am interested in: Explicitly describe a fundamental domain for t …

Suppose that $p$ is unramified in a number field $K$ of degree $n$. Apparently, Stickelberger proved that $\big( \frac{Disc(K)}{p}\big) = (-1)^{n - g}$, where $g$ is the number of prime ideal factors …

The Scholz reflection principle says, among other things, that if $D < 0$ is a negative fundamental discriminant, not $-3$, then the 3-ranks of the class group of $\mathbb{Q}(\sqrt{D})$ is either equa …

A little bit vague, but I hope useful for the entire community. I am, by training, an analytic number theorist. I have managed to learn some algebraic geometry, by reading parts of Silverman's Arithm …

I want to answer the following simple question: Given a three-dimensional ellipsoid defined by $Q(x, y, z) \leq Z$ for a positive definite quadratic form $Q$, how many lattice points in $\mathbb{Z …

While reading a number theory paper I encountered the identity $$ \int_{- \infty}^{\infty} (1 + x^2)^{ - \frac{z}{2} - 1} dx = \sqrt{\pi} \frac{ \Gamma(\frac{z + 1}{2}) }{\Gamma(\frac{z}{2} + 1)},$$ …