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

P. M. Gauthier; X. Xarles

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arXiv · 0911.5135

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

P. M. Gauthier·X. Xarles

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Abstract

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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P. M. Gauthier, X. Xarles. 2009-11-26. Perturbations of L-functions with or without non-trivial zeros off the critical line. https://arxiv.org/abs/0911.5135

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