An extension of the Linnik phenomenon. II

TL;DR

This paper extends the Linnik phenomenon to automorphic L-functions, showing that exceptional zeros influence a broader class of L-functions beyond Dirichlet cases.

Contribution

It generalizes the Linnik phenomenon to real analytic automorphic forms, revealing the repelling effect of exceptional zeros on these L-functions.

Findings

Exceptional zeros affect automorphic L-functions.

The extension involves significant notation changes.

Corrections and updates are included in this version.

Abstract

The (Deuring-Heilbronn-) Linnik phenomenon is extended to L-functions associated with real analytic automorphic forms. The repelling effect of exceptional zeros of Dirichlet L-functions are felt not only by those L-functions themselves but also by automorphic L-functions. This version 2 contains substantial changes of notation as well as a few corrections.