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 Tr. Mat. Inst. Steklova, 2000, Volume 228, Pages 76–89 (Mi tm492)

Adelic Formulas for Gamma and Beta Functions of One-Class Quadratic Fields: Applications to 4-Particle Scattering String Amplitudes

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 228, 67–80

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Citation: V. S. Vladimirov, “Adelic Formulas for Gamma and Beta Functions of One-Class Quadratic Fields: Applications to 4-Particle Scattering String Amplitudes”, Problems of the modern mathematical physics, Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov, Tr. Mat. Inst. Steklova, 228, Nauka, MAIK «Nauka/Inteperiodika», M., 2000, 76–89; Proc. Steklov Inst. Math., 228 (2000), 67–80

Citation in format AMSBIB
\Bibitem{Vla00} \by V.~S.~Vladimirov \paper Adelic Formulas for Gamma and Beta Functions of One-Class Quadratic Fields: Applications to 4-Particle Scattering String Amplitudes \inbook Problems of the modern mathematical physics \bookinfo Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov \serial Tr. Mat. Inst. Steklova \yr 2000 \vol 228 \pages 76--89 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm492} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1782573} \zmath{https://zbmath.org/?q=an:0993.11061} \transl \jour Proc. Steklov Inst. Math. \yr 2000 \vol 228 \pages 67--80 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Dragovich B., Volovich I.V., “p-Adic strings and noncommutativity”, Noncommutative Structures in Mathematics and Physics, NATO Science Series, Series II: Mathematics, Physics and Chemistry, 22, 2001, 391–399
2. V. S. Vladimirov, “Beta functions of local fields of characteristic zero. Applications to string amplitudes”, Izv. Math., 66:1 (2002), 41–57
3. A. A. Bolibrukh, A. A. Gonchar, I. V. Volovich, V. G. Kadyshevskii, A. A. Logunov, G. I. Marchuk, E. F. Mishchenko, S. M. Nikol'skii, S. P. Novikov, Yu. S. Osipov, L. D. Faddeev, D. V. Shirkov, “Vasilii Sergeevich Vladimirov (on his 80th birthday)”, Russian Math. Surveys, 58:1 (2003), 199–209
4. M. K. Kerimov, “Vasiliĭ Sergeevich Vladimirov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 43:11 (2003), 1541–1549
5. V. S. Vladimirov, “Adelic Formulas for Four-Particle String and Superstring Tree Amplitudes in One-Class Quadratic Fields”, Proc. Steklov Inst. Math., 245 (2004), 3–21
6. Dragovich B., “Non-archimedean geometry and physics on adelic spaces”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, 2004, 141–158
7. Aref'eva, IY, “Quantization of the Riemann zeta-function and cosmology”, International Journal of Geometric Methods in Modern Physics, 4:5 (2007), 881
8. S. V. Kozyrev, “Methods and Applications of Ultrametric and $p$-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84
9. A. Yu. Khrennikov, B. Nilsson, S. Nordebo, “Quantum rule for detection probability from Brownian motion in the space of classical fields”, Theoret. and Math. Phys., 174:2 (2013), 298–306
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