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- W2098132521 abstract "Let 𝔽q[t] denote the polynomial ring over the finite field 𝔽q. For c1, …, cs∈𝔽q[t]{0}, we consider the hypersurface H : c1z1k + … + cs zsk = 0. Let IP denote the subset of 𝔽q[t] containing all polynomials of degree strictly less than P. Let Ns, k, d, c(P) denote the number of d-tuples (x1,… ,xd) ∈ (IPs)d such that z = 𝔣1x1+…+𝔣d xd lies on H for all 𝔣1, …, 𝔣d∈𝔽q(t). In this paper, we apply a variant of the Hardy–Littlewood circle method to establish an asymptotic formula for Ns, k, d, c(P). As a consequence, we see that under certain conditions there are infinitely many d-dimensional rational spaces on H." @default.
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- W2098132521 date "2011-09-08" @default.
- W2098132521 modified "2023-09-27" @default.
- W2098132521 title "Asymptotic estimates for rational spaces on hypersurfaces in function fields" @default.
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- W2098132521 doi "https://doi.org/10.1112/plms/pdr031" @default.
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