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The value of polynomials represented by norm forms

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Abstract

Let P(t) be a product of (possibly repeated) linear factors over ℚ and K/ℚ an abelian extension. Under a strict condition, we show that the Brauer-Manin obstruction to the Hasse principle and weak approximation is the only one for any smooth proper model of the variety over ℚ defined by

$P(t) = N_{K/\mathbb{Q}} (x)$

.

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Authors and Affiliations

  1. State Key Laboratary of Mathematical Engineering and Advanced Computing, Zhengzhou, 450002, China

    Xin Wang

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  1. Xin Wang
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Correspondence to Xin Wang.

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Wang, X. The value of polynomials represented by norm forms. Sci. China Math. 57, 2525–2528 (2014). https://doi.org/10.1007/s11425-014-4894-z

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  • DOI: https://doi.org/10.1007/s11425-014-4894-z

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