Lethbridge Number Theory and Combinatorics Seminar: Kevin Henriot

  • Date: 10/27/2014
  • Time: 12:00
Kevin Henriot, UBC

University of Lethbridge


Linear equations in dense subsets of the squares


We discuss the solvability of certain linear equations in sparse subsets of the squares. Specifically, we investigate equations of the form \begin{align*}     \lambda_1 n_1^2 + \dotsb + \lambda_s n_s^2 = 0, \end{align*} where $s \geq 7$ and the coefficients $\lambda_i$ sum to zero and satisfy certain sign conditions. We show that such equations admit non-trivial solutions in any subset of $[N]$ of density $(\log N)^{-c_s}$, improving upon the previous best of $(\log\log N)^{-c}$.

Other Information: 
Location: B660 University Hall
Web page: http://www.cs.uleth.ca/~nathanng/ntcoseminar/