We present new estimates for sums of the divisor function and other similar arithmetic
functions in short intervals over function fields.(When the intervals are long, one obtains a …

We consider the variance of sums of arithmetic functions over random short intervals in the
function field setting. Based on the analogy between factorizations of random elements of F …

We propose a new heuristic approach to integral moments of L-functions over function fields,
which we demonstrate in the case of Dirichlet characters ramified at one place (the function …

We establish lower bounds for all weighted even moments of primes up to X in intervals
which are in agreement with a conjecture of Montgomery and Soundararajan. Our bounds …

For a fixed polynomial\varDelta Δ, we study the number of polynomials f of degree n over F
_q F q such that f and f+\varDelta f+ Δ are both irreducible, an F _q TF q T-analogue of the …

We use combinatorial methods to relate the expected values of polynomial factorization
statistics over to the cohomology of ordered configurations in as a representation of the …

This thesis consists of six chapters representing two directions of the author's graduate
research under the advisement of Jeffrey Lagarias and Michael Zieve. The first direction …

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This article is an overview of the vanishing cycles method in number theory over function
fields. We first explain how this works in detail in a toy example and then give three …

We investigate a function field analogue of a recent conjecture on autocorrelations of sums
of two squares by Freiberg, Kurlberg, and Rosenzweig, which generalizes an older …