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." (in German), Mathematische Zeitschrift 37: 405–415, doi:10.1007/BF01474583, ISSN 0025-5874 
• Heilbronn, Hans (1934), "On the class-number in imaginary quadratic fields.", Quarterly Journal of Mathematics 5: 150–160, doi:10.1093/qmath/os-5.1.150, Bibcode: 1934QJMat...5..150H 
• Montgomery, Hugh L. (1994), Ten lectures on the interface between analytic number theory and harmonic analysis, Regional Conference Series in Mathematics, 84, Providence, RI: American Mathematical Society, ISBN 978-0-8218-0737-8