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

Vladimirov, V. S.

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

Keywords:

regularized adelic formulas; open strings; closed strings; heterotic string