# 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.

In this note, I’ll discuss why square-root cancellation is so typical in problems in number theory and give a quick survey of important sums known or widely conjectured to satisfy bounds of this form.