The Deuring-Heilbronn phenomenon for Artin \(L\)-functions (Q2764528)

The Deuring-Heilbronn phenomenon for Dirichlet \(L\)-functions [see \textit{M. Deuring}, Math. Z. 37, 405-415 (1933; Zbl 0007.29602)] and \textit{H. Heilbronn} [Q. J. Math., Oxf. Ser. 5, 150-160 (1934; Zbl 0009.29602)]) consists of the observation that the existence of a zero of the \(L\)-series close to \(s = 1\) pushes the other zeros away from the line \(\sigma = 1\) [See \textit{J. C. Lagarias, H. L. Montgomery} and \textit{A. M. Odlyzko} [Invent. Math. 54, 271-296 (1979; Zbl 0413.12011)] for a version concerning Dedekind zeta functions). In this article the author shows that the same is true for general Artin \(L\)-functions: assuming Artin's conjecture, these \(L\)-functions are analytic except for a pole at \(s = 1\) if \(\chi\) contains the trivial character.