Deuring–Heilbronn phenomenon

In mathematics, the Deuring–Heilbronn phenomenon, discovered by Deuring (1933) and Heilbronn (1934), states that a counterexample to the generalized Riemann hypothesis for one Dirichlet L-function affects the location of the zeros of other Dirichlet L-functions.

See also

• Siegel zero

References

• Deuring, M. (1933), "Imaginäre quadratische Zahlkörper mit der Klassenzahl 1.",
  Zbl 0007.29602
• Heilbronn, Hans (1934), "On the class-number in imaginary quadratic fields.", Quarterly Journal of Mathematics, 5: 150–160,
  Zbl 0009.29602
• Zbl 0814.11001