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PreprintCC BY 4.0Zenodo

The Yousef L-Function: Corrections, the General Variable s, and the Generalized Redheffer Matrix

  • YOUSEF MUHAMMAD ALSAGHIR Al YOUSEF1
  1. 1Independent Researcher
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Abstract

We correct several numerical errors in the definition of the Yousef L-function

that appeared in an earlier preprint. We provide the correct values of Q(p) for odd

primes p ≤ 39, derive the corrected Euler product, and present the general formula

for the difference function D(s) = L(s, χ4) − LYousef(s) at an arbitrary complex

variable s. The coefficient c(n) = χ4(n)−G(n) takes values in {0, ±2, ±(1+i), ±(1−

i)}. After extracting the factor 2, we define Z(n) = 2/c(n) and prove the structural

identity ℜ(Z(n)) = χ4(n), valid for all s. This reveals that the non-periodicity of

the Yousef L-function is confined to the imaginary part of Z(n). We also establish

a generalized Redheffer determinant formula and provide a Mellin representation of

D(s) for all s with ℜ(s) > 1.

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Cite

BibTeXRIS
BibTeX
@misc{yousef2026yousef,
  title = {{The Yousef L-Function: Corrections, the General Variable s, and the Generalized Redheffer Matrix}},
  author = {YOUSEF MUHAMMAD ALSAGHIR Al YOUSEF},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23416249},
  url = {https://zenodo.org/records/23416249},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Yousef L-Function: Corrections, the General Variable s, and the Generalized Redheffer Matrix
AU  - YOUSEF MUHAMMAD ALSAGHIR Al YOUSEF
PY  - 2026
DA  - 2026/10/16
PB  - Zenodo
DO  - 10.5281/zenodo.23416249
UR  - https://zenodo.org/records/23416249
AB  - We correct several numerical errors in the definition of the Yousef L-function  that appeared in an earlier preprint. We provide the correct values of Q(p) for odd  primes p ≤ 39, derive the corrected Euler product, and present the general formula  for the difference function D(s) = L(s, χ4) − LYousef(s) at an arbitrary complex  variable s. The coefficient c(n) = χ4(n)−G(n) takes values in {0, ±2, ±(1+i), ±(1−  i)}. After extracting the factor 2, we define Z(n) = 2/c(n) and prove the structural  identity ℜ(Z(n)) = χ4(n), valid for all s. This reveals that the non-periodicity of  the Yousef L-function is confined to the imaginary part of Z(n). We also establish  a generalized Redheffer determinant formula and provide a Mellin representation of  D(s) for all s with ℜ(s) > 1.
ER  -