Differential equations properties and $\psi$ function - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

Differential equations properties and $\psi$ function

Résumé

Using the differential equations properties, we study the function $\psi$ which is a function defined by an integral. The particular case of this function coincide with the function $s\mapsto \zeta(s)/s$, where $\zeta$ is the Riemann Zeta function. In the end of the paper, we find that $\frac{\zeta(s)}{s}\neq -\frac{\zeta(1-s)}{1-s}$ for every $\Re(s)\in(0,\frac{1}{2})$ and $\Im(s)\in \mathbb{R}^*$. Thanks to the Riemann functional equation, we deduce that any "non-trivial zero" of $\zeta$ is of real part equal to $\frac{1}{2}$.
Fichier principal
Vignette du fichier
Oukil.pdf (97.92 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

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)

Identifiants

  • HAL Id : hal-03581978 , version 6

Citer

W Oukil. Differential equations properties and $\psi$ function. 2022. ⟨hal-03581978v6⟩
548 Consultations
124 Téléchargements

Partager

Gmail Facebook X LinkedIn More