Rigidity and Structural Asymmetry of Bounded Solutions
Résumé
In this manuscript, we introduce a family of parametrized nonhomogeneous linear complex differential equations on [1, ∞), depending on a complex parameter. We identify a Rotation number hypothesis on the non-homogeneous term, which establishes a structural asymmetry: if two solutions with the same initial condition equal to 1, corresponding respectively to the parameters s and 1 -s lying in the critical strip, are both bounded on [1, +∞), then ℜ(s) = 1 2 .
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