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TMF, 1993, Volume 94, Number 2, Pages 200–212 (Mi tmf1417)  

This article is cited in 5 scientific papers (total in 7 papers)

Vector addition theorems and Baker–Akhiezer functions

V. M. Buchstabera, I. M. Kricheverb

a All-Union Scientific Research Institute for Physical-Technical and Radiotechnical Measurements of USSR Gosstandart
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences

Abstract: Functional equations that arise naturally in various problems of modern mathematical physics are discussed. We introduce the concepts of an $N$-dimensional addition theorem for functions of a scalar argument and Cauchy equations of rank $N$ for a function of a $g$-dimensional argument that generalize the classical functional Cauchy equation. It is shown that for $N=2$ the general analytic solution of these equations is determined by the Baker–Akhiezer function of an algebraic curve of genus 2. It is also shown that functions give solutions of a Cauchy equation of rank $N$ for functions of a $g$-dimensional argument with $N\le 2^{g}$ in the case of a general $g$-dimensional Abelian variety and $N\le g$ in the case of a Jacobian variety of an algebra curve of genusg. It is conjectured that a functional Cauchy equation of rankg for a function of a $g$-dimensional argument is characteristic for functions of a Jacobian variety of an algebraic curve of genusg, i. e., solves the Riemann–Schottky problem.

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English version:
Theoretical and Mathematical Physics, 1993, 94:2, 142–149

Bibliographic databases:

Document Type: Article
Received: 08.05.1992

Citation: V. M. Buchstaber, I. M. Krichever, “Vector addition theorems and Baker–Akhiezer functions”, TMF, 94:2 (1993), 200–212; Theoret. and Math. Phys., 94:2 (1993), 142–149

Citation in format AMSBIB
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\paper Vector addition theorems and Baker--Akhiezer functions
\jour TMF
\yr 1993
\vol 94
\issue 2
\pages 200--212
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1221731}
\zmath{https://zbmath.org/?q=an:0803.39006}
\transl
\jour Theoret. and Math. Phys.
\yr 1993
\vol 94
\issue 2
\pages 142--149
\crossref{https://doi.org/10.1007/BF01019326}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1993LZ24300003}


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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. I. A. Taimanov, “Secants of Abelian varieties, theta functions, and soliton equations”, Russian Math. Surveys, 52:1 (1997), 147–218  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. J. Byatt-Smith, H. W. Braden, “On a Functional Equation of Ruijsenaars”, Theoret. and Math. Phys., 133:3 (2002), 1619–1630  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. A. Bolibrukh, A. P. Veselov, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, S. P. Novikov, T. E. Panov, Yu. M. Smirnov, “Viktor Matveevich Buchstaber (on his 60th birthday)”, Russian Math. Surveys, 58:3 (2003), 627–635  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. V. M. Buchstaber, D. V. Leikin, “Addition Laws on Jacobian Varieties of Plane Algebraic Curves”, Proc. Steklov Inst. Math., 251 (2005), 49–120  mathnet  mathscinet  zmath
    5. V. M. Buchstaber, I. M. Krichever, “Integrable equations, addition theorems, and the Riemann–Schottky problem”, Russian Math. Surveys, 61:1 (2006), 19–78  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. A. M. Vershik, A. P. Veselov, A. A. Gaifullin, B. A. Dubrovin, A. B. Zhizhchenko, I. M. Krichever, A. A. Mal'tsev, D. V. Millionshchikov, S. P. Novikov, T. E. Panov, A. G. Sergeev, I. A. Taimanov, “Viktor Matveevich Buchstaber (on his 70th birthday)”, Russian Math. Surveys, 68:3 (2013), 581–590  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. V. M. Buchstaber, “Cobordisms, manifolds with torus action, and functional equations”, Proc. Steklov Inst. Math., 302 (2018), 48–87  mathnet  crossref  crossref  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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