Year: 2026
Type: preprint
Abstract: We consider a class of Mellin transforms $\mu_\eta$ associated with a class of functions $\eta$, defined for every complex $s$ in the critical strip. We establish a sufficient condition on $\eta$ under which $\mu_\eta(s)$ and $\mu_\eta(1-s)$ cannot both vanish outside the critical line. An application is given to the case in which $\eta$ is the fractional part function, and the zeros of $\mu_\eta$ coincide with the zeros of the Riemann zeta function.
Author: Walid OUKIL
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W7214132807
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