diff 9506729..f6bf760 heilbronn_triangle_improvement_v2.txt
diff --git a/heilbronn_triangle_improvement_v2.txt b/heilbronn_triangle_improvement_v2.txt index d97051f..e34dd24 100644 --- a/heilbronn_triangle_improvement_v2.txt +++ b/heilbronn_triangle_improvement_v2.txt @@ -97,8 +97,8 @@ is tiny but positive. CPZ 2023 Delta(n) <= n^(-8/7 - 1/2000) for large n CPZ 2025 Delta(n) = O_eps(n^(-7/6+eps)) -Cohen, Pohoata, Zakharov 2023, cpz2023.pdf, https://arxiv.org/pdf/2305.18253v1 -Cohen, Pohoata, Zakharov 2025, cpz2025.pdf, https://arxiv.org/pdf/2409.07658v2 +Cohen, Pohoata, Zakharov 2023, ./pdf/cpz2023.pdf, https://arxiv.org/pdf/2305.18253v1 +Cohen, Pohoata, Zakharov 2025, ./pdf/cpz2025.pdf, https://arxiv.org/pdf/2409.07658v2 Two recent preprints assert stronger lower bounds. Ellmann (2025) declares in its abstract that the method is heuristic and gives in its @@ -108,8 +108,8 @@ attributed to it. Agama (2026) states an improved upper bound Delta(s) << s^(-2+eps) together with a corresponding improvement of the lower bound. -Ellmann 2025, ellmann.pdf, https://arxiv.org/pdf/1703.03297v12 -Agama 2026, agama.pdf, https://arxiv.org/pdf/2006.05269v13 +Ellmann 2025, ./pdf/ellmann.pdf, https://arxiv.org/pdf/1703.03297v12 +Agama 2026, ./pdf/agama.pdf, https://arxiv.org/pdf/2006.05269v13 The proof works with INTEGER COLUMNS u = (u_1, u_2, u_3)^T satisfying 0 <= u_1, u_2 < N and N <= u_3 < 2N. Each column represents the @@ -197,7 +197,7 @@ The two-sided bound is Minkowski's second theorem (Minkowski 1896, Geometrie der Zahlen, Section 50); a modern treatment is Henk (2002), Theorem 1.3. -Henk 2002, henk.pdf, https://arxiv.org/pdf/math/0204158v1 +Henk 2002, ./pdf/henk.pdf, https://arxiv.org/pdf/math/0204158v1 Lemma 2. Let L be a rank-two Euclidean lattice with successive lengths lambda_1 <= lambda_2.