A proof of the Landsberg-Schaar relation by finite methods
arXiv:1810.06172
Abstract
The Landsberg-Schaar relation is a classical identity between quadratic Gauss sums, normally used as a stepping stone to prove quadratic reciprocity. The Landsberg-Schaar relation itself is usually proved by carefully taking a limit in the functional equation for Jacobi's theta function. In this article we present a direct proof, avoiding any analysis.
Minor revision: added historical details and a discussion of closely related results. 13 pages. To appear in The Ramanujan Journal