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- W4313594997 abstract "Let $$qgeqslant 2$$ be a fixed prime power. We prove an asymptotic formula for counting the number of monic polynomials that are of degree n and have exactly k irreducible factors over the finite field $${mathbb {F}}_q$$ . We also compare our results with the analogous existing ones in the integer case, where one studies all the natural numbers up to x with exactly k prime factors. In particular, we show that the number of monic polynomials grows at a surprisingly higher rate when k is a little larger than $$log n$$ than what one would speculate from looking at the integer case." @default.
- W4313594997 created "2023-01-06" @default.
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- W4313594997 date "2023-01-04" @default.
- W4313594997 modified "2023-10-01" @default.
- W4313594997 title "On the distribution of polynomials having a given number of irreducible factors over finite fields" @default.
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- W4313594997 doi "https://doi.org/10.1007/s40993-022-00423-9" @default.
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