Description

• Title:
  Multiple zeta values and the WKB method
• Creator:
  Zakrzewski, Michał;
  Żołądek, Henryk
• Contributor:
  Krasiński, Tadeusz;
  Spodzieja, Stanisław;
  Institute of Mathematics, Jan Kochanowski University, ul. Świętokrzyska 15, 25-406 Kielce;
  Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw;
  zakrzewski@mimuw.edu.pl;
  zoladek@mimuw.edu.pl
• Description:
  The multiple zeta values ζ(d1, . . . , dr ) are natural generalizations of the values ζ(d) of the Riemann zeta functions at integers d. They have many applications, e.g. in knot theory and in quantum physics. It turns out that some generating functions for the multiple zeta values, like fd(x) = 1 − ζ(d)xd + ζ(d, d)x2d − . . . , are related with hypergeometric equations. More precisely, fd(x) is the value at t = 1 of some hypergeometric series dFd−1(t) = 1 − x t + . . ., a solution to a hypergeometric equation of degree d with parameter x. Our idea is to represent fd(x) as some connection coeffi- cient between certain standard bases of solutions near t = 0 and near t = 1. Moreover, we assume that |x| is large. For large complex x the above basic solutions are represented in terms of so-called WKB solutions. The series which define the WKB solutions are divergent and are subject to so-called Stokes phenomenon. Anyway it is possible to treat them rigorously. In the paper we review our results about application of the WKB method to the generating functions f x), focusing on the cases d = 2 and d = 3.
• Object availability:
  free access
• Rights:
  Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska;
  http://creativecommons.org/licenses/by-nc-nd/3.0/pl ;
  © Copyright by University of Łódź, Łódź 2013
• Date:
  2017.12.13;
  2013
• Type:
  Book chapter
• Language:
  English
• Format:
  application/pdf;
  image/jpeg
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Krasiński T., Spodzieja S. (eds.), Analytic and Algebraic Geometry, Łódź University Press, Łódź 2013;
• Identifier:
  Zakrzewski M., Żołądek H, Multiple zeta values and the WKB, [in:] Krasiński T., Spodzieja S. (eds.), Analytic and Algebraic Geometry, Łódź University Press, Łódź 2013, s. 155-202, doi: 10.18778/7969-017-6.12;
  978-83-7969-017-6;
  http://hdl.handle.net/11089/23613 ;
  10.18778/7969-017-6.12
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  seek permission
• Type:
  text