A generic effective Oppenheim theorem for systems of forms

DOI10.1016/j.jnt.2020.07.002zbMath1467.11063arXiv2003.06114OpenAlexW3048399265MaRDI QIDQ2004948

Jiyoung Han, Anish Ghosh, Prasuna Bandi

Publication date: 7 October 2020

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.06114

zbMATH Keywords

geometry of numberseffective Oppenheim conjectureRogers' second moment theoremsystems of quadratic and linear forms

Mathematics Subject Classification ID

Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Diophantine approximation in probabilistic number theory (11K60) Mean value and transfer theorems (11H60)

Related Items (7)

Explicit solutions to the Oppenheim conjecture forindefinite ternary diagonal forms ⋮ Rogers' mean value theorem for \(S\)-arithmetic Siegel transforms and applications to the geometry of numbers ⋮ Khintchine-type theorems for values of subhomogeneous functions at integer points ⋮ Values of inhomogeneous forms at S ‐integral points ⋮ Second moment of the light-cone Siegel transform and applications ⋮ Inhomogeneous Diophantine approximation for generic homogeneous functions ⋮ Quantitative Oppenheim conjecture for \(S\)-arithmetic quadratic forms of rank \(3\) and \(4 \)

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