Counting Integral Points Near Space Curves: A Fourier Analytic Approach
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DOI: 10.1093/imrn/rnaf200
Abstract: We establish upper and lower bounds for the number of integral points which lie within a neighbourhood of a smooth nondegenerate curve in $\mathbb{R}^{n}$ for $n\geqslant 3$. These estimates are new for $n\geqslant 4$, and… read more here.
Keywords: integral points; fourier analytic; points near; space curves ... See more keywords
Trace Formula for Integral Points on the Three-Dimensional Sphere
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DOI: 10.1134/s1064562420010044
Abstract: Abstract Average values over integral points on a three-dimensional sphere with an arbitrary smooth weight function are studied. For them, an expansion of the mean product of two L-series associated with the Hecke basis in… read more here.
Keywords: three dimensional; dimensional sphere; points three; formula integral ... See more keywords