Abstract
We establish the Hasse principle for systems of r simultaneous diagonal cubic equations whenever the number of variables exceeds 6r and the associated coefficient matrix contains no singular \(r\times r\) submatrix, thereby achieving the theoretical limit of the circle method for such systems.
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21 June 2023
A Correction to this paper has been published: https://doi.org/10.1007/s00208-023-02645-3
Notes
Henceforth we adopt the convention that zero entries in a matrix are left blank.
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Acknowledgments
The authors are grateful to the referees for the extreme care taken in reviewing this paper, and in particular for numerous suggestions which have clarified our exposition and prompted significant corrections.
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The authors are grateful to the Hausdorff Research Institute for Mathematics in Bonn for excellent working conditions that made the writing of this paper feasible. The support of the Akademie der Wissenschaften zu Göttingen is also gratefully acknowledged.
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Brüdern, J., Wooley, T.D. The Hasse principle for systems of diagonal cubic forms. Math. Ann. 364, 1255–1274 (2016). https://doi.org/10.1007/s00208-015-1249-1
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DOI: https://doi.org/10.1007/s00208-015-1249-1