Number theory

Some new results on the higher energies

I. Shkredov

Journal of Number Theory 281, 110 (2026)

Generalising the recent Kelley–Meka result on sets avoiding arithmetic progressions of length three leads to developments in the theory of the higher energies.

Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"
Image for the paper "Some new results on the higher energies I"