# Quadratic Reciprocity and the Theta Function

One of the better-known proofs of quadratic reciprocity involves the Gauss sums. This post gives a variant proof which motivates the introduction of Gauss sums using the Jacobi theta function.

This post discusses two classic problems in analytic number theory: the Gauss circle problem and the Dirichlet divisor problem.

These problems are known to be related at a deep level, a fact which is often missed at first glance because the obvious/early attacks on them look quite different.

In this post, I compare these “trivial” estimates, and show how Gauss’ estimate can be realized using a few different techniques.