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We prove estimates for the level of distribution of the Mobius function, von Mangoldt function, and divisor functions in squarefree progressions in the ring of polynomials over a finite field. Each level of distribution converges to $1$ as $q$ goes to $infty$, and the power savings converges to square-root cancellation as $q$ goes to $infty$. These results in fact apply to a more general class of functions, the factorization functions, that includes these three. The divisor estimates have applications to the moments of $L$-functions, and the von Mangoldt estimate to one-level densities.
Using geometric methods, we improve on the function field version of the Burgess bound, and show that, when restricted to certain special subspaces, the M{o}bius function over $mathbb F_q[T]$ can be mimicked by Dirichlet characters. Combining these,
Let F/F_q be an algebraic function field of genus g defined over a finite field F_q. We obtain new results on the existence, the number and the density of dimension zero divisors of degree g-k in F where k is a positive integer. In particular, for q=
In this paper, we examine how far a polynomial in $mathbb{F}_2[x]$ can be from a squarefree polynomial. For any $epsilon>0$, we prove that for any polynomial $f(x)inmathbb{F}_2[x]$ with degree $n$, there exists a squarefree polynomial $g(x)inmathbb{F
We study the existence of non-special divisors of degree $g$ and $g-1$ for algebraic function fields of genus $ggeq 1$ defined over a finite field $F_q$. In particular, we prove that there always exists an effective non-special divisor of degree $gge
The Cancellation Problem for Affine Spaces is settled affirmatively, that is, it is proved that : Let $ k $ be an algebraically closed field of characteristic zero and let $n, m in mathbb{N}$. If $R[Y_1,..., Y_m] cong_k k[X_1,..., X_{n+m}]$ as $k$-al