Abstract
Let \(f_1, \ldots , f_r\) be regular indefinite integral quadratic forms with s prime variables. We investigate the values taken by real linear combinations of \(f_1, \ldots , f_r\). It is proved that, under certain conditions, the values of the real linear combinations of three general quadratic forms, with 6 prime variables in total, can approximate any real numbers. The previous results of this type focus on diagonal forms.
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Acknowledgements
The author would like to thank the referee for many valuable comments and detailed suggestions that helped improve the quality of this manuscript substantially, and to thank Wenbin Zhu for useful discussion.
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Communicated by Tim Browning.
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Liu, H. The values of general quadratic forms at prime arguments. Monatsh Math 201, 465–482 (2023). https://doi.org/10.1007/s00605-022-01793-z
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DOI: https://doi.org/10.1007/s00605-022-01793-z