Geodesic
Adelic Formulas for Gamma and Beta Functions of One-Class Quadratic Fields: Applications to 4-Particle Scattering String Amplitudes
Informatics and Automation, Problems of the modern mathematical physics, Tome 228 (2000), pp. 76-89

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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. 
@article{TRSPY_2000_228_a6,
     author = {V. S. Vladimirov},
     title = {Adelic {Formulas} for {Gamma} and {Beta} {Functions} of {One-Class} {Quadratic} {Fields:} {Applications} to {4-Particle} {Scattering} {String} {Amplitudes}},
     journal = {Informatics and Automation},
     pages = {76--89},
     publisher = {mathdoc},
     volume = {228},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2000_228_a6/}
}
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V. S. Vladimirov. Adelic Formulas for Gamma and Beta Functions of One-Class Quadratic Fields: Applications to 4-Particle Scattering String Amplitudes. Informatics and Automation, Problems of the modern mathematical physics, Tome 228 (2000), pp. 76-89. http://geodesic.mathdoc.fr/item/TRSPY_2000_228_a6/