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arXiv · 2603.15716

Asymmetry of a class of Mellin transforms via bounded solutions

Walid Oukil
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Abstract

We introduce a family of parametrized non-homogeneous linear complex differential equations on $[1,\infty)$, depending on a complex parameter $s$ in the critical strip. We identify sufficient conditions on the non-homogeneous term that induce a structural asymmetry between the solutions corresponding to the parameters $s$ and $1-s$. More precisely, if both solutions with initial value $1$ are bounded on $[1,\infty)$, then necessarily $\Re(s)=\tfrac12$. The initial condition associated with the unique bounded solution corresponding to a parameter $s$ represents a zero of the Mellin transform associated with the non-homogeneous term at the point $s$.

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Walid Oukil. 2026-09-14. Asymmetry of a class of Mellin transforms via bounded solutions. https://arxiv.org/abs/2603.15716

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