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Theoretical and Mathematical Physics

, Volume 94, Issue 2, pp 142–149 | Cite as

Vector addition theorems and Baker-Akhiezer functions

  • V. M. Bukhshtaber
  • I. M. Krichever
Article

Abstract

Functional equations that arise naturally in various problems of modern mathematical physics are discussed. We introduce the concepts of anN-dimensional addition theorem for functions of a scalar argument and Cauchy equations of rankN for a function of ag-dimensional argument that generalize the classical functional Cauchy equation. It is shown that forN=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 θ functions give solutions of a Cauchy equation of rankN for functions of ag-dimensional argument withN≤2 g in the case of a generalg-dimensional Abelian variety andNg 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 ag-dimensional argument is characteristic for θ functions of a Jacobian variety of an algebraic curve of genusg, i.e., solves the Riemann—Schottky problem.

Keywords

Mathematical Physic Functional Equation Abelian Variety Algebraic Curve Vector Addition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • V. M. Bukhshtaber
  • I. M. Krichever

There are no affiliations available

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