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1. CMB 2015 (vol 58 pp. 673)

Achter, Jeffrey; Williams, Cassandra
 Local Heuristics and an Exact Formula for Abelian Surfaces Over Finite Fields Consider a quartic $q$-Weil polynomial $f$. Motivated by equidistribution considerations, we define, for each prime $\ell$, a local factor that measures the relative frequency with which $f\bmod \ell$ occurs as the characteristic polynomial of a symplectic similitude over $\mathbb{F}_\ell$. For a certain class of polynomials, we show that the resulting infinite product calculates the number of principally polarized abelian surfaces over $\mathbb{F}_q$ with Weil polynomial $f$. Keywords:abelian surfaces, finite fields, random matricesCategory:14K02

2. CMB Online first

Totik, Vilmos
 Universality under SzegÅ's condition This paper presents a theorem on universality on orthogonal polynomials/random matrices under a weak local condition on the weight function $w$. With a new inequality for polynomials and with the use of fast decreasing polynomials, it is shown that an approach of D. S. Lubinsky is applicable. The proof works at all points which are Lebesgue-points both for the weight function $w$ and for $\log w$. Keywords:universality, random matrices, Christoffel functions, asymptotics, potential theoryCategories:42C05, 60B20, 30C85, 31A15
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