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Student Solves a Long-Standing Problem About the Limits of Addition
A new proof illuminates the hidden patterns that emerge when addition becomes impossible.
“The longer it went without people being able to improve on that simple bound, the more cachet this problem acquired,” said Ben Green, Bedert’s doctoral adviser at Oxford. But Bedert thought it might be useful to prove something more attainable: that even if these sets aren’t literally built from arithmetic progressions, they share certain key, progression-like properties. He represented the structure of his sets using a tool called the Fourier transform, and then modified a 1981 proof to show that some of the individual components of that representation must have a large Littlewood norm.
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