A quantitative Oppenheim theorem for generic ternary quadratic forms

Anish Ghosh; Dubi Kelmer

doi:10.3934/jmd.2018001

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2018, Volume 12: 1-8. Doi: 10.3934/jmd.2018001

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A quantitative Oppenheim theorem for generic ternary quadratic forms

Anish Ghosh^1, and
Dubi Kelmer^2,

1.
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
2.
Department of Mathematics, Boston College, Chestnut Hill, MA 02467-3806, USA

Received: February 26, 2017

Revised: November 09, 2017

Published: November 2017

AG: Partially supported by ISF-UGC. DK: Partially supported by NSF grant DMS-1401747.

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Abstract

We prove a quantitative version of Oppenheim's conjecture for generic ternary indefinite quadratic forms. Our results are inspired by and analogous to recent results for diagonal quadratic forms due to Bourgain [3].

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Mathematics Subject Classification: Primary: 11E20; Secondary: 37A17.

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