• 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