Let f be a {0,1}-cosine polynomial with n terms. In his 1986 monograph, J.E. Littlewood considered the minimum number of zeros that such polynomials have in [0,2π] and conjectured that the number of such roots is “n-1 or not much less”. While it is now known that there exist cosine polynomials with considerably fewer roots, much less is known about the lower bound and, in fact, it was a long standing problem just to show that the number of such zeros tends to infinity with n. We will discuss the resolution of this conjecture and also mention some more recent progress on the upper bound.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
