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- W3105548828 abstract "We estimate the covariance in counts of almost-primes in $mathbb{F}_q[T]$, weighted by higher-order von Mangoldt functions. The answer takes a pleasant algebraic form. This generalizes recent work of Keating and Rudnick that estimates the variance of primes, and makes use, as theirs, of a recent equidistribution result of Katz. In an appendix we prove some related identities for random matrix statistics, which allows us to give a quick proof of a $2times2$ ratio theorem for the characteristic polynomial of the unitary group. We additionally identify arithmetic functions whose statistics mimic those of hook Schur functions." @default.
- W3105548828 created "2020-11-23" @default.
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- W3105548828 date "2014-07-22" @default.
- W3105548828 modified "2023-10-18" @default.
- W3105548828 title "The Covariance of Almost-Primes in 𝔽q[T]" @default.
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- W3105548828 doi "https://doi.org/10.1093/imrn/rnu118" @default.
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