Work

Asymmetry of a class of Mellin transforms: Request for counterexamples

Year: 2026

Type: preprint

Abstract: We study a class of Mellin transforms $\mu_\eta$ associated with functions $\eta$ and investigate the distribution of their zeros in the critical strip. Under suitable assumptions on $\eta$, we obtain a condition preventing $\mu_\eta(s)$ and $\mu_\eta(1-s)$ from vanishing simultaneously away from the critical line when the imaginary part of $s$ is sufficiently large. We formulate a statement and invite the reader to exhibit a counterexample.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.24141105

Author: OUKIL, Walid

Institution: University of Sciences and Technology Houari Boumediene

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225782752

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