Pré-Publication, Document De Travail Année : 2026

Asymmetry of Generalized $\zeta$ Functions under the Rotation Number Hypothesis

Résumé

In this manuscript, we show that the Riemann zeta function satisfies $\big(\zeta(s),\zeta(1-\overline{s})\big)\neq(0,0)$ for any $s$ in the critical strip, except on the critical line. This still holds even when the fractional part function is replaced by a function satisfying a specific \textit{Rotation Number Hypothesis}.

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Dates et versions

hal-03581978 , version 1 (20-02-2022)
hal-03581978 , version 2 (23-02-2022)
hal-03581978 , version 3 (27-02-2022)
hal-03581978 , version 4 (09-03-2022)
hal-03581978 , version 5 (05-04-2022)
hal-03581978 , version 6 (07-04-2022)
hal-03581978 , version 7 (14-04-2022)
hal-03581978 , version 8 (19-04-2022)
hal-03581978 , version 9 (27-04-2022)
hal-03581978 , version 10 (28-04-2022)
hal-03581978 , version 11 (29-04-2022)
hal-03581978 , version 12 (07-05-2022)
hal-03581978 , version 13 (10-07-2022)
hal-03581978 , version 14 (17-07-2022)
hal-03581978 , version 15 (23-07-2022)
hal-03581978 , version 16 (27-07-2022)
hal-03581978 , version 17 (05-10-2022)
hal-03581978 , version 18 (10-10-2022)
hal-03581978 , version 19 (20-10-2022)
hal-03581978 , version 20 (25-10-2022)
hal-03581978 , version 21 (01-11-2022)
hal-03581978 , version 22 (07-11-2022)
hal-03581978 , version 23 (11-10-2023)
hal-03581978 , version 24 (26-10-2023)
hal-03581978 , version 25 (26-11-2023)
hal-03581978 , version 26 (17-11-2025)
hal-03581978 , version 27 (08-12-2025)
hal-03581978 , version 28 (03-01-2026)
hal-03581978 , version 29 (18-01-2026)
hal-03581978 , version 30 (21-01-2026)
hal-03581978 , version 31 (23-01-2026)
hal-03581978 , version 32 (28-01-2026)
hal-03581978 , version 33 (17-02-2026)
hal-03581978 , version 34 (17-02-2026)
hal-03581978 , version 35 (01-03-2026)
hal-03581978 , version 36 (06-03-2026)
hal-03581978 , version 37 (09-03-2026)
hal-03581978 , version 38 (12-03-2026)
hal-03581978 , version 39 (18-04-2026)

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  • HAL Id : hal-03581978 , version 39

Citer

W Oukil. Asymmetry of Generalized $\zeta$ Functions under the Rotation Number Hypothesis. 2026. ⟨hal-03581978v39⟩

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