Family 004Number theoryNo LeanNot yet digestedfeatured
Hilbert’s tenth problem over ℚ
Proves that no algorithm decides whether an integer-coefficient polynomial in an arbitrary number of variables has a rational zero, resolving Hilbert's tenth problem over ℚ negatively.
Manuscripts in this family · 2
Hilbert’s tenth problem over the rational numbers
Oct 6, 2026·main.pdf
We give a negative answer to Hilbert's tenth problem over the rational numbers: no algorithm decides whether a polynomial with integer coefficients has a rational zero. The number of variables is part of the input.
A pointwise 2-converse for elliptic curves with rational two-torsion
Oct 7, 2026·paper.pdf
We prove a pointwise 2-converse for elliptic curves over with nonzero rational two-torsion: if the -Selmer corank is zero or one, then the analytic rank and Mordell–Weil rank equal that corank, and the Shafarevich–Tate group is finite. The result allows arbitrary reduction at 2.