Concatenation theorems for the Gowers uniformity norms, and applications Terence Tao 2015

Terence Tao, University of California, Los Angeles Concatenation theorems for the Gowers uniformity norms, and applications Abstract: Abstract: A function P(n, m) of two variables which is a polynomial of degree less than d1 in the n variable, and a polynomial of degree less than d2 in the m variable, is automatically a polynomial of degree less than d1 + d2 1 jointly in the n, m variables. In joint work with Tamar Ziegler, we generalise this concatenation of degrees phenomenon to the Gowers unifomity