# On a conjecture of Gowers and Wolf

@inproceedings{Altman2021OnAC, title={On a conjecture of Gowers and Wolf}, author={Daniel Altman}, year={2021} }

: Gowers and Wolf have conjectured that, given a set of linear forms { ψ i } ti = 1 each mapping Z D to Z , if s is an integer such that the functions ψ s + 1 i ,..., ψ s + 1 t are linearly independent, then averages of the form E x ∏ ti = 1 f ( ψ i ( x )) may be controlled by the Gowers U s + 1 -norm of f . We prove (a stronger version of) this conjecture.

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