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- W2125227452 abstract "By adopting a new approach to the analysis of the density of p-adic solutions arising in applications of the circle method, we show that under modest conditions the existence of non-trivial p-adic solutions suffices to establish positivity of the singular series. This improves on earlier approaches due to Davenport, Schmidt and others, and allows us to establish an asymptotic formula for the number of simultaneous zeros of non-singular pairs of cubic forms in at least 131 variables. As a by-product, we obtain a version of Hensel's Lemma for linear spaces." @default.
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- W2125227452 date "2015-04-03" @default.
- W2125227452 modified "2023-10-18" @default.
- W2125227452 title "A note on p -adic solubility for forms in many variables" @default.
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- W2125227452 doi "https://doi.org/10.1112/blms/bdv023" @default.
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