You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
We use generating functions to relate the expected values of polynomial factorization statistics over @math to the cohomology of ordered configurations in @math as a representation of the symmetric group. Our methods lead to a new proof of the twisted Grothendieck-Lefschetz formula for squarefree polynomial factorization statistics of Church, Ellenberg, and Farb.

Cited Abstract(s):
[1]: We study the distribution in short intervals of certain arithmetic functions, including the von Mangoldt function and the M "obius function, on polynomials over a finite field @math . Using the Grothendieck-Lefschetz trace formula, we reinterpret each moment of these distributions as a point-counting problem on a highly singular complete intersection variety. We compute part of the @math -adic cohomology of these varieties, yielding an asymptotic bound on each moment for fixed degree @math in the limit as @math .
There have been other generalizations of Theorem from squarefree polynomials to all polynomials. Gadish [Sec. 1.3] Gadish and Hast, Matei [1] both study expected values of functions defined on the set of all polynomials; their functions depend on both the degree of the irreducible factors and their multiplicities. We call these . Gadish [Cor. 1.4] Gadish shows that the expected value of a weighted factorization statistic @math on @math matches the expected value of @math on @math viewed as a class function. Stated geometrically, the expected values of weighted factorization statistics on degree @math polynomials correspond to the cohomology of @math as an @math -representation, while the expected values of our factorization statistics correspond to the cohomology of @math as an @math -representation.