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.

• Siegel zero

• Deuring, M. (1933), "Imaginäre quadratische Zahlkörper mit der Klassenzahl 1.", Mathematische Zeitschrift (in German), 37: 405–415, doi:10.1007/BF01474583, ISSN 0025-5874, JFM 59.0946.03, Zbl 0007.29602
• Heilbronn, Hans (1934), "On the class-number in imaginary quadratic fields.", Quarterly Journal of Mathematics, 5: 150–160, Bibcode:1934QJMat...5..150H, doi:10.1093/qmath/os-5.1.150, JFM 60.0155.01, Zbl 0009.29602
• Montgomery, Hugh L. (1994), Ten lectures on the interface between analytic number theory and harmonic analysis, Regional Conference Series in Mathematics, vol. 84, Providence, RI: American Mathematical Society, ISBN 978-0-8218-0737-8, Zbl 0814.11001