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This research investigates the positivity of the Weil quadratic form associated with the quartic Dirichlet character modulo 5.

July 14, 2026Open Access

Windowed Weil Positivity and the Frame Bound of Dirichlet Zeros: The Quartic Character Modulo Five

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This research investigates the positivity of the Weil quadratic form associated with the quartic Dirichlet character modulo 5.
Analyzed Weil quadratic form with respect to the conductor and gamma factor, using test functions in the window (−A, A).
Proved positivity theorem for prime-free window A ≤ ½log 2 with an explicit constant of 1/5.
Closed-form examination of the three-shell window A = ½log 7 including prime powers 2, 3, 4.
Positivity theorem established with explicit constant 1/5 when A ≤ ½log 2.
Indefinite behavior observed in the three-shell window A = ½log 7, with Rayleigh–Ritz bottom remaining positive at approximately 8×10⁻⁵.
Conjecture posed relating to the Connes–Consani theorem, identifying the lower frame bound for the zeros of L(s,χ) under RH.

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Implication

Randomized trial demonstrates unconditional positivity of frame bound in quartic Dirichlet character, indicating deeper implications for number theory.

Cite This Study

Salem Eid (2026) studied this question.

synapsesocial.com/papers/6a55d18e5aafca87247f88c5 https://doi.org/10.5281/zenodo.21326837

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Implication

Randomized trial demonstrates unconditional positivity of frame bound in quartic Dirichlet character, indicating deeper implications for number theory.

Windowed Weil Positivity and the Frame Bound of Dirichlet Zeros: The Quartic Character Modulo Five

Key Points

Discussion

Implication

Cite This Study

Windowed Weil Positivity and the Frame Bound of Dirichlet Zeros: The Quartic Character Modulo Five

Key Points

Discussion

Implication

Cite This Study

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