Thue equations that simultaneously fail the Hasse principle

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.

References in corpus (2)

• A positive proportion of locally soluble quartic Thue equations are globally insoluble
• Thue inequalities with few coefficients