Vs. Vladimirov et Tm. Sapuzhak, ADELIC FORMULAS FOR STRING AMPLITUDES IN FIELDS OF ALGEBRAIC-NUMBERS, letters in mathematical physics, 37(2), 1996, pp. 233-242
On the basis of the analysis on adele groups (Tate's formula) for any
field of algebraic numbers, a regularization of infinite adelic produc
ts of gamma and beta functions of local fields is proposed. The formul
as obtained are applied to representations of the four-point crossing
symmetric Veneziano and Virasoro-Shapiro amplitudes through regularize
d adelic products of the corresponding string (open and closed, resp.)
amplitudes.