Multiple sums with the Möbius function

Key Points

• This research aims to establish bounds for bilinear sums involving the Möbius function, particularly in relation to equations.
• Analyzed bilinear sums involving the Möbius function across various equations.
• Compared findings to analogues of the ternary Goldbach problem.
• Explored restrictions on the third variable to investigate binary sums.
• Established nontrivial bounds for certain bilinear sums.
• Showed that results are consistent with the complexity of the binary Goldbach problem.
• Made partial progress in bounding binary sums, albeit limited.