The average number of integral points on the congruent number curves
Chan S. 2024. The average number of integral points on the congruent number curves. Advances in Mathematics. 457, 109946.
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Abstract
We show that the total number of non-torsion integral points on the elliptic curves ED : y
2 = x3 − D2x, where D ranges over positive squarefree integers less than N, is O(N(log N)
−1/4+ǫ). The proof involves a discriminant-lowering procedure on integral binary quartic forms and an application of Heath-Brown’s method on estimating the average size of the 2-Selmer group of the curves in this family.
Publishing Year
Date Published
2024-09-11
Journal Title
Advances in Mathematics
Publisher
Elsevier
Volume
457
Article Number
109946
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eISSN
IST-REx-ID
Cite this
Chan S. The average number of integral points on the congruent number curves. Advances in Mathematics. 2024;457. doi:10.1016/j.aim.2024.109946
Chan, S. (2024). The average number of integral points on the congruent number curves. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2024.109946
Chan, Stephanie. “The Average Number of Integral Points on the Congruent Number Curves.” Advances in Mathematics. Elsevier, 2024. https://doi.org/10.1016/j.aim.2024.109946.
S. Chan, “The average number of integral points on the congruent number curves,” Advances in Mathematics, vol. 457. Elsevier, 2024.
Chan S. 2024. The average number of integral points on the congruent number curves. Advances in Mathematics. 457, 109946.
Chan, Stephanie. “The Average Number of Integral Points on the Congruent Number Curves.” Advances in Mathematics, vol. 457, 109946, Elsevier, 2024, doi:10.1016/j.aim.2024.109946.
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