Geodesic
Derivation of Freund--Witten adelic formula for four-point Veneziano amplitudes
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 3, pp. 355-367

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. 
@article{TMF_1993_94_3_a0,
     author = {V. S. Vladimirov},
     title = {Derivation of {Freund--Witten} adelic formula for four-point {Veneziano} amplitudes},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {355--367},
     publisher = {mathdoc},
     volume = {94},
     number = {3},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_94_3_a0/}
}
TY  - JOUR
AU  - V. S. Vladimirov
TI  - Derivation of Freund--Witten adelic formula for four-point Veneziano amplitudes
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1993
SP  - 355
EP  - 367
VL  - 94
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1993_94_3_a0/
LA  - ru
ID  - TMF_1993_94_3_a0
ER  - 
%0 Journal Article
%A V. S. Vladimirov
%T Derivation of Freund--Witten adelic formula for four-point Veneziano amplitudes
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1993
%P 355-367
%V 94
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1993_94_3_a0/
%G ru
%F TMF_1993_94_3_a0
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/