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- W2267160987 abstract "Although eta quotients have been extensively studied for a long time,the fundamental problem of constructing an algorithm that determines whether or not a given holomorphic eta quotient $f$ is a product of two holomorphic eta quotients other than 1 and itself still remains open. The difficulty of the problem stems from an apparent lack of information about the existence of an upper bound for the levels of the factors of $f$. Here we show that if a holomorphic eta quotient $f$ of level $N$ has no nontrivial factors whose level divide $N$, then the levels of all the factors of $f$ are bounded above with respect to $N$. We also provide an explicit upper bound in terms of $N$ for the minimum of the levels of the nontrivial factors of $f$. This bound has a further refinement with respect to the weight of $f$. In particular, we show that any reducible holomorphic eta quotient of a prime power level $N$ has a nontrivial factor whose level divides $N$. As a consequence, it follows that all rescalings by positive integers and all Atkin-Lehner involutions of irreducible holomorphic eta quotients of prime power levels are irreducible." @default.
- W2267160987 created "2016-06-24" @default.
- W2267160987 creator A5081114895 @default.
- W2267160987 date "2016-02-09" @default.
- W2267160987 modified "2023-09-27" @default.
- W2267160987 title "Algorithmic determination of irreducibility of holomorphic eta quotients" @default.
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