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Adelic formulas for gamma and beta functions of one class number quadratic fields: Applications to 4-particle scattering string amplitudes. (English. Russian original) Zbl 0993.11061
Proc. Steklov Inst. Math. 228, 67-80 (2000); translation from Tr. Mat. Inst. Steklova 228, 76-89 (2000).
Summary: Regularized adelic formulas for gamma and beta functions for arbitrary quasicharacters (either ramified or not) and in an arbitrary field of algebraic numbers are concretized as applied to one-class quadratic fields (and to the field of rational numbers). Applications to 4-tachyon tree string amplitudes, to the Veneziano (open strings) and Virasoro (closed strings) amplitudes as well as to massless 4-particle amplitudes of the Ramond-Neveu-Schwarz superstring and a heterotic string are discussed. Certain relations between different superstring amplitudes are established.
For the entire collection see [Zbl 0952.00070].

##### MSC:
 11R47 Other analytic theory 11R56 Adèle rings and groups 11S80 Other analytic theory (analogues of beta and gamma functions, $$p$$-adic integration, etc.) 11Z05 Miscellaneous applications of number theory 33E50 Special functions in characteristic $$p$$ (gamma functions, etc.) 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory