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- W4296566654 abstract "A central question in Arithmetic geometry is to determine for which polynomials $f in mathbb{Z}[t]$ and which number fields $K$ the Hasse principle holds for the affine equation $f(t) = N_{K/mathbb{Q}}(boldsymbol{x}) neq 0$. Whilst extensively studied in the literature, current results are largely limited to polynomials and number fields of low degree. In this paper, we establish the Hasse principle for a wide family of polynomials and number fields, including polynomials that are products of arbitrarily many linear, quadratic or cubic factors. The proof generalises an argument of Irving, which makes use of the beta sieve of Rosser and Iwaniec. As a further application of our sieve results, we prove new cases of a conjecture of Harpaz and Wittenberg on locally split values of polynomials over number fields, and discuss consequences for rational points in fibrations." @default.
- W4296566654 created "2022-09-21" @default.
- W4296566654 creator A5081556920 @default.
- W4296566654 date "2022-09-19" @default.
- W4296566654 modified "2023-09-25" @default.
- W4296566654 title "Polynomials represented by norm forms via the beta sieve" @default.
- W4296566654 doi "https://doi.org/10.48550/arxiv.2209.08949" @default.
- W4296566654 hasPublicationYear "2022" @default.
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