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  "body": "\n## Summary\n\nA Siegel zero, or Landau–Siegel zero, is a hypothetical real zero of a [[Dirichlet L-function|9D2Z543EJQ]] of a real character that lies very close to $1$.\nThe classical zero-free region for Dirichlet L-functions excludes every zero near $s = 1$ except possibly one such zero.\nWhether Siegel zeros exist is open; the [[generalized Riemann hypothesis|DNKA4WBKDS]] rules them out.\nTheir possible existence is the source of ineffective constants in results such as the [[Siegel–Walfisz theorem|XEPW251A97]].\n\n## Explanations\n\n### L1 human\n\nDirichlet L-functions are cousins of the Riemann zeta function, one for each Dirichlet character.\nTheir zeros control how primes are spread over residue classes.\nOne knows that no zero comes very close to the point $s = 1$, with one possible exception: a single real zero for a real character.\nThat possible exception is called a Siegel zero.\nNobody has found one, and most experts believe they do not exist, but nobody can rule them out either.\n",
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