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- W4312122038 abstract "The van der Waerden's Conjecture states that the set $mathscr{P}_{n,N}^0(mathbb{Q})$ of monic integer polynomials $f(X)$ of degree $n$, with height $le N$ such that the Galois group $G_{K_f/mathbb{Q}}$ of the splitting field $K_f/mathbb{Q}$ is the full symmetric group, has order $|mathscr{P}_{n,N}^0(mathbb{Q})|=(2N)^n+O_n(N^{n-1})$ as $Nrightarrow+infty$. The conjecture has been shown previously for cubic and quartics polynomials by van der Waerden, Chow and Dietmann. Subsequently, Bhargava proved it for $nge6$. In this paper, we generalize the result for polynomials with coefficients in the ring of algebraic integers $mathcal{O}_K$ of a fixed finite extension $K/mathbb{Q}$ of degree $d$, for some values of $n$ and $d$." @default.
- W4312122038 created "2023-01-04" @default.
- W4312122038 creator A5044072478 @default.
- W4312122038 date "2022-12-22" @default.
- W4312122038 modified "2023-09-30" @default.
- W4312122038 title "Towards a generalization of the van der Waerden's conjecture for Sn-polynomials with integral coefficients over a fixed number field extension" @default.
- W4312122038 doi "https://doi.org/10.48550/arxiv.2212.11608" @default.
- W4312122038 hasPublicationYear "2022" @default.
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