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Formulas for the limiting distribution of traces of Frobenius

By Gilles Lachaud

We discuss the distribution of the trace of a random matrix in the compact Lie group USp2g, with the normalized Haar measure. According to the generalized Sato-Tate conjecture, if A is an abelian variety of dimension g defined over the rationals, the sequence of traces of Frobenius in the successive reductions of A modulo primes appears to be equidistributed with respect to this distribution. If g = 2, we provide expressions for the characteristic function, the density, and the repartition function of this distribution in terms of higher transcendental functions, namely Legendre and Meijer functions.

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Citation data

  • DOI 10.24350/CIRM.V.18478403
  • Cite this video Lachaud, Gilles (11/02/2014). Formulas for the limiting distribution of traces of Frobenius. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18478403
  • URL https://dx.doi.org/10.24350/CIRM.V.18478403


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