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Siegel zero
Potential counterexample to the generalized Riemann hypothesis
Siegel zero
In mathematics, more specifically in the field of analytic number theory, a Landau–Siegel zero or simply Siegel zero, also known as an exceptional zero, named after Edmund Landau and Carl Ludwig Siegel, was a type of potential counterexample to the generalized Riemann hypothesis, on the zeros of Dirichlet L-functions associated to quadratic number fields. Roughly speaking, these would be possible zeros very near (in a quantifiable sense) to s = 1 {\displaystyle s=1} . In 2026, OpenAI released a large number of manuscripts which included a claimed AI-generated proof of the non-existence of Siegel zeros; these arguments have since been simplified and restated by, among others, William Banks, Bryce Kerr, Ben Green, and Terence Tao.
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