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PreprintCC BY-NC-ND 4.0HAL

Asymmetry of a class of Mellin transforms: Request for Counterexamples

  • Walid Oukil
Open at sourcePDFCite

Abstract

We study a class of Mellin transforms μη associated with functions η and investigate the distribution of their zeros in the critical strip. Under suitable assumptions on η, we obtain a condition preventing μη(s) and μη(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.

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Cite

BibTeXRIS
BibTeX
@misc{oukil2026asymmetry,
  title = {{Asymmetry of a class of Mellin transforms: Request for Counterexamples}},
  author = {Walid Oukil},
  howpublished = {HAL},
  year = {2026},
  month = jun,
  url = {https://hal.science/hal-05640414v8},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Asymmetry of a class of Mellin transforms: Request for Counterexamples
AU  - Walid Oukil
PY  - 2026
DA  - 2026/06/01
PB  - HAL
UR  - https://hal.science/hal-05640414v8
AB  - We study a class of Mellin transforms μ_η associated with functions η and investigate the distribution of their zeros in the critical strip. Under suitable assumptions on η, we obtain a condition preventing μ_η(s) and μ_η(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.
ER  -