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math.NT2026
Quantitative Oppenheim Conjecture for Random Quadratic Forms and Optimal Variance Bounds in Function Fields
Jiyoung Han, Noy Soffer Aranov
We prove a quantitative version of Oppenheim's conjecture in the function field setting. In order to do so, we compute the higher moments of the Siegel transform. In particular, we…
math.NT2020
A generic effective Oppenheim theorem for systems of forms
Prasuna Bandi, Anish Ghosh, Jiyoung Han
We prove a uniform effective density theorem as well as an effective counting result for a generic system comprising a polynomial with a mild homogeneous condition and several line…