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## Abstract

We present two complementary methods, each applicable in a different range, to evaluate the distribution of the lowest eigenvalue of random matrices in a Jacobi ensemble. The first method solves an associated Painlevé VI nonlinear differential equation numerically, with suitable initial conditions that we determine. The second method proceeds via constructing the power-series expansion of the Painlevé VI function. Our results are applied in a forthcoming paper in which we model the distribution of the first zero above the central point of elliptic curve L-function families of finite conductor and of conjecturally orthogonal symmetry.

Translated title of the contribution | The lowest eigenvalue of Jacobi random matrix ensembles and Painleve VI |
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Original language | English |

Pages (from-to) | 405204 - 405230 |

Number of pages | 27 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 43, number 40 |

DOIs | |

Publication status | Published - Oct 2010 |

### Bibliographical note

Publisher: IOP## Fingerprint

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