Siegel zero

Summary

A Siegel zero, or Landau–Siegel zero, is a hypothetical real zero of a Dirichlet L-function of a real character that lies very close to $1$. The classical zero-free region for Dirichlet L-functions excludes every zero near $s = 1$ except possibly one such zero. Whether Siegel zeros exist is open; the generalized Riemann hypothesis rules them out. Their possible existence is the source of ineffective constants in results such as the Siegel–Walfisz theorem.