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Izv. RAN. Ser. Mat., 1996, Volume 60, Issue 1, Pages 63–86 (Mi izv62)  

This article is cited in 11 scientific papers (total in 13 papers)

Adelic formulae for the gamma and beta functions of completions of algebraic number fields, and applications of them to string amplitudes

V. S. Vladimirov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: On the basis of analysis on the adele group (the Tate formula) of an algebraic number field, a regularization is constructed for the divergent adelic products of the gamma and beta functions of all (non-isomorphic) completions of this field. The formulae obtained are applied to representations of the four-point crossing-symmetric Veneziano amplitudes and Virasoro–Shapiro amplitudes in terms of regularized adelic products of string amplitudes (for open or closed strings) corresponding to all non-Archimedean completions of the algebraic number field under consideration.

DOI: https://doi.org/10.4213/im62

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English version:
Izvestiya: Mathematics, 1996, 60:1, 67–90

Bibliographic databases:

Document Type: Article
MSC: Primary 11S80, 11R56; Secondary 81T30, 83E30, 33B15
Received: 11.09.1995

Citation: V. S. Vladimirov, “Adelic formulae for the gamma and beta functions of completions of algebraic number fields, and applications of them to string amplitudes”, Izv. RAN. Ser. Mat., 60:1 (1996), 63–86; Izv. Math., 60:1 (1996), 67–90

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Vladimirov V.S., “Adelic formulas for gamma- and beta-functions in algebraic number fields”, Vestnik Moskovskogo Universiteta Seriya 1 Matematika Mekhanika, 1996, no. 6, 11–12  zmath  isi
    2. Vladimirov V.S., “Adelic formulas for gamma- and beta-functions in fields of algebraic numbers”, Doklady Akademii Nauk, 347:1 (1996), 11–15  mathnet  mathscinet  zmath  isi
    3. S. A. Albeverio, J. M. Bayod, C. Perez-Garsia, A. Yu. Khrennikov, R. Cianci, “Non-Archimedean analogues of orthogonal and symmetric operators”, Izv. Math., 63:6 (1999), 1063–1087  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Albeverio S., Bayod J.M., Perez-Garcia C., Cianci R., Khrennikov A., “Non-archimedean analogues of orthogonal and symmetric operators and p-adic quantization”, Acta Applicandae Mathematicae, 57:3 (1999), 205–237  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. V. S. Vladimirov, “Adelic Formulas for Gamma and Beta Functions of One-Class Quadratic Fields: Applications to 4-Particle Scattering String Amplitudes”, Proc. Steklov Inst. Math., 228 (2000), 67–80  mathnet  mathscinet  zmath
    6. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    7. M. K. Kerimov, “Vasiliĭ Sergeevich Vladimirov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 43:11 (2003), 1541–1549  mathnet  mathscinet
    8. 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  mathnet  mathscinet  zmath
    9. 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  mathnet  crossref  crossref  zmath  isi  elib
    10. V. S. Vladimirov, “Regularized adelic formulas for string and superstring amplitudes in one-class quadratic fields”, Theoret. and Math. Phys., 164:3 (2010), 1101–1109  mathnet  crossref  crossref  adsnasa  isi
    11. Kosyak A.V. Khrennikov A.Yu. Shelkovich V.M., “Pseudodifferential Operators on Adele Rings and Wavelet Bases”, Dokl. Math., 85:3 (2012), 358–362  crossref  mathscinet  zmath  isi  elib  elib  scopus
    12. Kosyak A.V. Khrennikov A.Yu. Shelkovich V.M., “Wavelet Bases on Adele Rings”, Dokl. Math., 85:1 (2012), 75–79  crossref  mathscinet  zmath  isi  elib  elib  scopus
    13. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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