1
Introduction
▶
Proof outline
Notation
2
Reduction to Diophantine equations
3
Upper bounds for integer points
▶
3.1
Fourier analysis
3.2
Geometry of numbers
3.3
Determinant method
4
Combining the upper bounds
▶
4.1
Preliminaries
4.2
Summary of the main bounds
4.3
Completion of the upper bound for \(\nu \)
▶
Case 1: Assume \(s_2\ge 0.3\).
Subcase 1.1: Assume \(b_3\le 0.34-s_1-s_2+\delta \).
Subcase 1.2: Assume \(b_3{\gt} 0.34-s_1-s_2+\delta \).
Case 2: Assume \(s_2{\lt} 0.3\).
Subcase \(\bf {2.1}\): Assume \(a_3\geq 0.32\)
Subcase \(\mathbf{2.2}\): Assume \(b_3+c_3{\lt}0.33-\frac{s_2}{2}-\frac{\delta }{2}\).
Subcase \(\mathbf{2.3}\): Assume \(4s_1+3s_2{\gt}0.71\).
Subcase \(\mathbf{2.4}\): Assume \(4s_1+s_2{\lt}0.4\).
Subcase \(\mathbf{2.5}\): Assume \(0.066\leq s_2\leq 0.204\).
Subcase \(\mathbf{2.6}\): Assume \(2s_1-s_2{\gt}0.025\).
5
Bibliography
Dependency graph
ABCExceptions
Jared Duker Lichtman and Bhavik Mehta
1
Introduction
Proof outline
Notation
2
Reduction to Diophantine equations
3
Upper bounds for integer points
3.1
Fourier analysis
3.2
Geometry of numbers
3.3
Determinant method
4
Combining the upper bounds
4.1
Preliminaries
4.2
Summary of the main bounds
4.3
Completion of the upper bound for \(\nu \)
Case 1: Assume \(s_2\ge 0.3\).
Subcase 1.1: Assume \(b_3\le 0.34-s_1-s_2+\delta \).
Subcase 1.2: Assume \(b_3{\gt} 0.34-s_1-s_2+\delta \).
Case 2: Assume \(s_2{\lt} 0.3\).
Subcase \(\bf {2.1}\): Assume \(a_3\geq 0.32\)
Subcase \(\mathbf{2.2}\): Assume \(b_3+c_3{\lt}0.33-\frac{s_2}{2}-\frac{\delta }{2}\).
Subcase \(\mathbf{2.3}\): Assume \(4s_1+3s_2{\gt}0.71\).
Subcase \(\mathbf{2.4}\): Assume \(4s_1+s_2{\lt}0.4\).
Subcase \(\mathbf{2.5}\): Assume \(0.066\leq s_2\leq 0.204\).
Subcase \(\mathbf{2.6}\): Assume \(2s_1-s_2{\gt}0.025\).
5
Bibliography