#### Alladi Ramakrishnan Hall

#### Effective Quantitative Oppenheim for almost every quadratic form

#### Jayadev Athreya

##### University of Illinois at Urbana-Champaign

*In 1986, Margulis, using methods from dynamics, proved A. Oppenheim's 1929 conjecture that for every indefinite irrational quadratic form in at least 3 variables, the values it takes at integer lattice points form a dense subset of the real line. Subsequently, Eskin-Margulis-Mozes proved an associated counting result, giving polynomial asymptotics for the number of lattice points of norm at most T which get mapped to a fixed interval. In joint work with Margulis, we give an effective version if this result for almost every quadratic form.*

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