Geodesic
Derivation of Freund–Witten adelic formula for four-point Veneziano amplitudes
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 3, pp. 355-367 
V. S. Vladimirov. Derivation of Freund–Witten adelic formula for four-point Veneziano amplitudes. Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 3, pp. 355-367. http://geodesic.mathdoc.fr/item/TMF_1993_94_3_a0/
@article{TMF_1993_94_3_a0,
     author = {V. S. Vladimirov},
     title = {Derivation of {Freund{\textendash}Witten} adelic formula for four-point {Veneziano} amplitudes},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {355--367},
     year = {1993},
     volume = {94},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_94_3_a0/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

On the base of analysis on the adelic group (Teyte Tate's formula) a regularization is proposed for the divergent infiniteproduct of $p$-adic $\Gamma$-functions $$ \Gamma _p(\alpha )=\frac {1-p^{\alpha -1}}{1-p^{-\alpha }}\,, \quad p=2,3,5,\dots \,. $$ Adelic formula $$ \,{\operatorname {reg}}\,\prod _{p=2}^\infty \Gamma _p(\alpha )=\frac {\zeta (\alpha )}{\zeta (1-\alpha )}, $$ ($\zeta (\alpha )$ is Riemann $\zeta$-function) is proved.

[1] Freund P. G. O., Witten E., Phys. Lett.(B), 199:2 (1987), 191–194 | DOI | MR

[2] Volovich I. V., Lett. in Math. Phys., 16 (1988), 61–67 | DOI | MR | Zbl

[3] Aref'eva I. Ya., Dragovic B. G., Volovich I. V., Phys. Lett.(B), 209:4 (1988), 445–450 | DOI | MR

[4] Borevich Z. I., Shafarevich I. R., Teoriya chisel, Nauka, M., 1966 | MR

[5] Schikhof W. H., Ultrametric calculus. An introduction to $p$-adic analysis, Cambridge Univ. Press, 1984 | MR | Zbl

[6] Vladimirov V. S., Volovich I. V., Zelenov E. I., $P$-Adic Analysis in Mathematical Physics, World Scientific, Singapore, 1993 | MR

[7] Gelfand I. M., Graev M. I., Pyatetskii-Shapiro I. I., Teoriya predstavlenii i avtomorfnye funktsii, Nauka, M., 1966 | MR

[8] Gelfand I. M., Shilov G. E., Obobschennye funktsii i deistviya nad nimi, Fizmatgiz, M., 1958 | MR

[9] Volovich I. V., TMF, 71:3 (1987), 337–340 | MR | Zbl

[10] Volovich I.V., Class. Quantum Grav., 4 (1987), L83–L87 | DOI | MR

[11] Freund P. G. O., Olson M., Phys. Lett.(B), 199:2 (1987), 186–190 | DOI | MR

[12] Frampton P. H., Okada Y., Phys. Rev. Lett., 60 (1988), 484–486 | DOI | MR