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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
mathematics
High order Fuchsian equations for the square lattice Ising model: 5
Journal of Physics A: Mathematical and Theoretical, Volume 42, No. 27, Article 275209, Year 2009
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Description
We consider the Fuchsian linear differential equation obtained (modulo a prime) for , the five-particle contribution to the susceptibility of the square lattice Ising model. We show that one can understand the factorization of the corresponding linear differential operator from calculations using just a single prime. A particular linear combination of and can be removed from and the resulting series is annihilated by a high order globally nilpotent linear ODE. The corresponding (minimal order) linear differential operator, of order 29, splits into factors of small orders. A fifth-order linear differential operator occurs as the left-most factor of the 'depleted' differential operator and it is shown to be equivalent to the symmetric fourth power of LE, the linear differential operator corresponding to the elliptic integral E. This result generalizes what we have found for the lower order terms and . We conjecture that a linear differential operator equivalent to a symmetric (n - 1) th power of LE occurs as a left-most factor in the minimal order linear differential operators for all 's. © 2009 IOP Publishing Ltd.
Authors & Co-Authors
Bostan, Alin
France, Le Chesnay
Inria Institut National de Recherche en Informatique et en Automatique
Boukraa, Salah
Algeria, Blida
Université Blida 1
Guttmann, A. J.
Australia, Melbourne
University of Melbourne
Hassani, Saoud
Algeria, Algiers
Commissariat à L'energie Atomique
Jensen, I.
Australia, Melbourne
University of Melbourne
Maillard, Jean Marie
France, Paris
Université Paris Cité
Zenine, Nadjah
Algeria, Algiers
Commissariat à L'energie Atomique
Statistics
Citations: 38
Authors: 7
Affiliations: 5
Identifiers
Doi:
10.1088/1751-8113/42/27/275209
ISSN:
17518113
e-ISSN:
17518121