We study sums of Dirichlet characters over polynomials in $\mathbb{F}_q[t]$ with a prescribed number of irreducible factors. Our main results are explicit formulae for these sums in terms of zeros of Dirichlet L-functions. We also exhibit new phenomena concerning Chebyshev-type biases of such sums when the number of irreducible factors is very large.
Analogues of the Balog--Wooley Decomposition for Subsets of Finite Fields and Character Sums with Convolutions
Character sums over elements of extensions of finite fields with restricted coordinates
Character sums over shifted primes
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