Abstract
By applying Schmidt’s lattice method, we prove results on simultaneous Diophantine approximation modulo 1 for systems of polynomials in a single prime variable provided that certain local conditions are met.
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Notes
In the introduction of [10], the definition of jointly intersective polynomials is not correctly stated. We would like to take this opportunity to point out this mistake and rectify it.
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Acknowledgments
The authors would like to thank Roger Baker, Andrew Granville, Ben Green, and Terence Tao for helpful conversations. They are also thankful to the referee for useful comments which help to improve the presentation of the paper.
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Communicated by J. Schoißengeier.
The research of the second author is supported in part by NSA Young Investigator Grants #H98230-10-1-0155 and #H98230-12-1-0220.
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Lê, T.H., Spencer, C.V. Intersective polynomials and Diophantine approximation, II. Monatsh Math 177, 79–99 (2015). https://doi.org/10.1007/s00605-014-0665-8
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DOI: https://doi.org/10.1007/s00605-014-0665-8