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arXiv · 2607.05234

Thue equations that simultaneously fail the Hasse principle

Paloma Bengoechea
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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 >2 and are ordered by the absolute value of the maximum of the coefficients.

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Paloma Bengoechea. 2026-07-06. Thue equations that simultaneously fail the Hasse principle. https://doi.org/10.1017/s0305004121000323

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