On square-free values of large polynomials over the rational function field

We investigate the density of square-free values of polynomials with large coefficients over the rational function field 𝔽 q [t]. Some interesting questions answered as special cases of our results include the density of square-free polynomials in short intervals, and an asymptotic for the number of representations of a large polynomial N as a sum of a k-th power of a small polynomial and a square-free polynomial.

The autocorrelation of the Möbius function and Chowla's conjecture for the rational function field in characteristic 2

We prove a function field version of Chowla's conjecture on the autocorrelation of the Möbius function in the limit of a large finite field of characteristic 2, extending previous work in odd characteristic.

Quotients of trees for arithmetic subgroups of PGL2 over a rational function field

In this note we determine the structure of the quotient of the Bruhat–Tits tree of the locally compact group PGL

THE FOURTH MOMENT OF DIRICHLET L-FUNCTIONS FOR THE RATIONAL FUNCTION FIELD

We study the moments of the Dirichlet L-function when defined over the polynomial ring over finite fields. We obtain an asymptotic formula of the fourth moment for the central value of these Dirichlet L-functions. In addition, we find a lower bound for the 2k th moment of these L-functions. These results agree up to constants with the polynomial ring analog of the Keating and Snaith Conjecture for the asymptotic of leading terms.