On the distribution of the trace in the unitary symplectic group and the\n distribution of Frobenius

2015/06/22 by Gilles Lachaud, Lachaud, Gilles · 1 citation
Mathematics · #Advanced Algebra and Geometry #Graph theory and applications #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.1506.06482

Abstract

The purpose of this article is to study the distribution of the trace on the\nunitary symplectic group. We recall its relevance to equidistribution results\nfor the eigenvalues of the Frobenius in families of abelian varieties over\nfinite fields, and to the limiting distribution of the number of points of\ncurves. We give four expressions of the trace distribution if g = 2, in terms\nof special functions, and also an expression of the distribution of the trace\nin terms of elementary symmetric functions. In an appendix, we prove a formula\nfor the trace of the exterior power of the identity representation.\n

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