On some mathematical equations concerning the functions z (s) and z (s,w) and some Ramanujan-type series for 1/pigreco. Mathematical connections with some equations concerning the p-adic open string for the scalar tachyon field and the zeta strings.
Questo il mio ultimo lavoro sulle connessioni tra Teoria delle Stringhe e Teoria dei Numeri. Qui di seguito l'Abstract ed il link dell'articolo pubblicato sul Database di Fisica e Teoria dei Numeri del Prof. Watkins, per chi volesse leggerlo per intero.
In this paper, in the Section 1, we have described some equations concerning the functions z (s) and z (s,w). In this Section, we have described also some equations concerning a transformation formula involving the gamma and Riemann zeta functions of Ramanujan. Furthermore, we have described also some mathematical connections with various theorems concerning the incomplete elliptic integrals described in the “Ramanujan’s lost notebook”. In the Section 2, we have descrive some Ramanujan-type series for 1/pigreco and some equations concerning the p-adic open string for the scalar tachyon field. In this Section, we have described also some possible and interesting mathematical connections with some Ramanujan’s Theorems, contained in the first letter of Ramanujan to G. H. Hardy. In the Section 3, we have described some equations concerning the zeta strings and the zeta nonlocal scalar fields. In conclusion, in the Section 4, we have showed some possible mathematical connections between the arguments above mentioned, the Palumbo-Nardelli model and the Ramanujan’s modular equations that are related to the physical vibrations of the bosonic strings and of the superstrings.