English

A proof of the Landsberg-Schaar relation by finite methods

Number Theory 2019-07-18 v2

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.

Keywords

Cite

@article{arxiv.1810.06172,
  title  = {A proof of the Landsberg-Schaar relation by finite methods},
  author = {Ben Moore},
  journal= {arXiv preprint arXiv:1810.06172},
  year   = {2019}
}

Comments

Minor revision: added historical details and a discussion of closely related results. 13 pages. To appear in The Ramanujan Journal