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Thue equations that simultaneously fail the Hasse principle

Part of: Diophantine equations

Published online by Cambridge University Press:  17 May 2021

PALOMA BENGOECHEA
PALOMA BENGOECHEA*
Affiliation:
ETH Zürich, Department of Mathematics, Rämistrasse 101, 8092Zürich, Switzerland. e-mails: paloma.bengoechea@math.ethz.ch
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Abstract

We refine a previous construction by Akhtari and Bhargava so that, for every positive integer m, we obtain a positive proportion of Thue equations F(x, y) = h that fail the integral Hasse principle simultaneously for every positive integer h less than m. The binary forms F have fixed degree ≥ 3 and are ordered by the absolute value of the maximum of the coefficients.

MSC classification

Primary: 11D59: Thue-Mahler equations 11D75: Diophantine inequalities
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 172 , Issue 3 , May 2022 , pp. 617 - 626
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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Footnotes

†

Supported by SNF grant 173976.

References

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