Anne de Roton

Define $e_{n}(t)=\{t/n\}$. Let $d_N$ denote the distance in $L^2(0,\infty ; t^{-2}dt)$ between the indicator function of $[1,\infty[$ and the vector space generated by $e_1, \dots, e_N$. A theorem of B\'aez-Duarte (2003) states that the Riemann...

In 1953, K. Roth proved that any subset of positive integers of positive density contains infinitely many non-trivial three-term arithmetic progressions. (By a non-trivial arithmetic progression we mean one of the form (a, a+d, a+2d) with d > 0.)...