Lethbridge Number Theory and Combinatorics Seminar: Allysa Lumley

Let q≡1(mod4) be a prime power and Fq be the finite field with q elements. Let 1/2<σ<1 be fixed. We consider D a monic square-free polynomial in Fq[T] and χD the Kronecker symbol associated with D. In this talk, we will discuss the distribution of large values of logL(σ,χD) with D varying over monic square-free polynomials with degree n→∞. We will highlight the expected similarities to the situation over quadratic extensions of Q as well as the surprising differences.