A generic effective Oppenheim theorem for systems of forms

JOURNAL OF NUMBER THEORY

卷:218

Article

Bandi, Prasuna¹  Ghosh, Anish¹  Han, Jiyoung² 

[1] Tata Inst Fundamental Res, Sch Math, Mumbai 400005, Maharashtra, India

[2] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

关键词: Effective Oppenheim conjecture;    Systems of quadratic and linear forms;    Geometry of numbers;    Rogers' second moment theorem;   

DOI  :  10.1016/j.jnt.2020.07.002

来源: Elsevier

【 摘 要 】

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 Rogers' second moment formula for the Siegel transform on the space of unimodular lattices. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free