A generic effective Oppenheim theorem for systems of forms

2020/03/13 by Bandi, Prasuna, Ghosh, Anish, Han, Jiyoung · 2 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2003.06114

Abstract

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 linear forms using Roger's second moment formula for the Siegel transform on the space of unimodular lattices.

Cited by

• Distribution of values at tuples of integer vectors under symplectic forms
• A survey and a result on inhomogeneous quadratic forms

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