### Abstract

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 L_{E}, 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 L_{E} occurs as a left-most factor in the minimal order linear differential operators for all 's.

Original language | English |
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Article number | 275209 |

Number of pages | 33 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 27 |

DOIs | |

Publication status | Published - 1 Jan 2009 |

Externally published | Yes |

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## Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*42*(27), [275209]. https://doi.org/10.1088/1751-8113/42/27/275209