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TMF, 1993, Volume 94, Number 3, Pages 355–367 (Mi tmf1427)  

This article is cited in 3 scientific papers (total in 5 papers)

Derivation of Freund–Witten adelic formula for four-point Veneziano amplitudes

V. S. Vladimirov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: On the base of analysis on the adelic group (Teyte Tate's formula) a regularization is proposed for the divergent infiniteproduct of $p$-adic $\Gamma$-functions
$$ \Gamma _p(\alpha )=\frac {1-p^{\alpha -1}}{1-p^{-\alpha }} , \quad p=2,3,5,… . $$
Adelic formula
$$  {\operatorname {reg}} \prod _{p=2}^\infty \Gamma _p(\alpha )=\frac {\zeta (\alpha )}{\zeta (1-\alpha )}, $$
($\zeta (\alpha )$ is Riemann $\zeta$-function) is proved.

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English version:
Theoretical and Mathematical Physics, 1993, 94:3, 251–259

Bibliographic databases:

Document Type: Article
Received: 17.11.1992

Citation: V. S. Vladimirov, “Derivation of Freund–Witten adelic formula for four-point Veneziano amplitudes”, TMF, 94:3 (1993), 355–367; Theoret. and Math. Phys., 94:3 (1993), 251–259

Citation in format AMSBIB
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\by V.~S.~Vladimirov
\paper Derivation of Freund--Witten adelic formula for four-point Veneziano amplitudes
\jour TMF
\yr 1993
\vol 94
\issue 3
\pages 355--367
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1226216}
\zmath{https://zbmath.org/?q=an:0916.11062}
\transl
\jour Theoret. and Math. Phys.
\yr 1993
\vol 94
\issue 3
\pages 251--259
\crossref{https://doi.org/10.1007/BF01017255}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993MA71000001}


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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. V. S. Vladimirov, “Freund–Witten adelic formulae for Veneziano and Virasoro–Shapiro amplitudes”, Russian Math. Surveys, 48:6 (1993), 1–39  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. 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. Math., 60:1 (1996), 67–90  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. M. K. Kerimov, “Vasiliĭ Sergeevich Vladimirov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 43:11 (2003), 1541–1549  mathnet  mathscinet
    5. S. V. Kozyrev, A. Yu. Khrennikov, V. M. Shelkovich, “$p$-Adic wavelets and their applications”, Proc. Steklov Inst. Math., 285 (2014), 157–196  mathnet  crossref  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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