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Advances in Mathematical Physics
Volume 2010 (2010), Article ID 941560, 44 pages
http://dx.doi.org/10.1155/2010/941560
Research Article

Renormalization, Isogenies, and Rational Symmetries of Differential Equations

1INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, France
2LPTHIRM and Département d'Aéronautique, Université de Blida, 09470 Blida, Algeria
3Centre de Recherche Nucléaire d'Alger, 2 Boulevard. Frantz Fanon, BP 399, 16000 Alger, Algeria
4LPTMC, UMR 7600 CNRS, Université de Paris, Tour 24, 4ème étage, case 121, 4 Place Jussieu, 75252 Paris Cedex 05, France
5XLIM, Université de Limoges, 123 avenue Albert Thomas, 87060 Limoges Cedex, France
6St Petersburg Department of Steklov Institute of Mathematics, 27 Fontanka, 191023 St. Petersburg, Russia

Received 21 December 2009; Accepted 17 January 2010

Academic Editor: Richard Kerner

Copyright © 2010 A. Bostan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Citations to this Article [5 citations]

The following is the list of published articles that have cited the current article.

  • A. Bostan, S. Boukraa, S. Hassani, M. van Hoeij, J-M Maillard, J-A Weil, and N. Zenine, “The Ising model: from elliptic curves to modular forms and Calabi-Yau equat ions,” Journal of Physics A-Mathematical and Theoretical, vol. 44, no. 4, 2011. View at Publisher · View at Google Scholar
  • M. Assis, S. Boukraa, S. Hassani, M. van Hoeij, J-M Maillard, and B. M. McCoy, “Diagonal Ising susceptibility: elliptic integrals, modular forms and Calabi -Yau equations,” Journal of Physics A-Mathematical and Theoretical, vol. 45, no. 7, 2012. View at Publisher · View at Google Scholar
  • S Boukraa, S Hassani, and J-M Maillard, “ Holonomic functions of several complex variables and singularities of anisotropic Ising n -fold integrals ,” Journal of Physics A: Mathematical and Theoretical, vol. 45, no. 49, pp. 494010, 2012. View at Publisher · View at Google Scholar
  • A. Bostan, S. Boukraa, G. Christol, S. Hassani, and J-M Maillard, “Ising n-fold integrals as diagonals of rational functions and integrality o f series expansions,” Journal of Physics A-Mathematical and Theoretical, vol. 46, no. 18, 2013. View at Publisher · View at Google Scholar
  • S Boukraa, S Hassani, J-M Maillard, and J-A Weil, “Differential algebra on lattice Green functions and Calabi–Yau operators,” Journal of Physics A: Mathematical and Theoretical, vol. 47, no. 9, pp. 095203, 2014. View at Publisher · View at Google Scholar