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.

References

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, 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, 84, Providence, RI: American Mathematical Society, ISBN 0-8218-0737-4, Zbl 0814.11001

This article is issued from Wikipedia - version of the 8/20/2013. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.