Perturbations of L-functions with or without non-trivial zeros off the critical line

Details Perturbations of L-functions with or without non-trivial zeros off the critical line Perturbations of L-functions with or without non-trivial zeros off the critical line

2009-11-26

arxiv.org/abs/0911.5135v1

Mathematics

Complex Variables

To appear in Proceedings of the Wurzburg Conference "New Directions In The Theory Of Universal ZETA- And L-Functions", 6-10 Oc

Scientific paper

There exist small perturbations of L-functions, satisfying the appropriate
functional equation, for which the analogue of the Riemann hypothesis fails
radically. Moreover, this phenomenon is generic. However, there also exist
small perturbations, for which the analogue of the Riemann hypothesis holds.

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