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- W4288363867 abstract "Given an arithmetic function $a: mathbb{N} rightarrow mathbb{R}$, one can associate a naturally defined, doubly infinite family of Jensen polynomials. Recent work of Griffin, Ono, Rolen, and Zagier shows that for certain families of functions $a: mathbb{N} rightarrow mathbb{R}$, the associated Jensen polynomials are eventually hyperbolic (i.e., eventually all of their roots are real). This work proves Chen, Jia, and Wang's conjecture that the partition Jensen polynomials are eventually hyperbolic as a special case. Here, we make this result explicit. Let $N(d)$ be the minimal number such that for all $n geq N(d)$, the partition Jensen polynomial of degree $d$ and shift $n$ is hyperbolic. We prove that $N(3)=94$, $N(4)=206$, and $N(5)=381$, and in general, that $N(d) leq (3d)^{24d} (50d)^{3d^{2}}$." @default.
- W4288363867 created "2022-07-29" @default.
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- W4288363867 date "2019-04-29" @default.
- W4288363867 modified "2023-10-18" @default.
- W4288363867 title "Hyperbolicity of the partition Jensen polynomials" @default.
- W4288363867 doi "https://doi.org/10.48550/arxiv.1904.12727" @default.
- W4288363867 hasPublicationYear "2019" @default.
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