Let x be an algebraic number. Lehmer's problem predicts that the product of the degree of x and the Weil height of x is bounded by an absolute constant. The basic idea to tackle this problem is to study the points of small Weil height (or short, small points) in an algebraic closure of Q. The case where small points of an algebraic field L are either 0 or a root of unity is intensively studied and we will provide a few explicit examples. Then we will explain why it is complicated to precisely locate small points of L if the latter contains more small points than 0 and the roots of unity. Time permitting, we will discuss about Lehmer's problem on elliptic curves.
This is a periodic series seminar organized by members and postdoctors of Morningside Center of Mathematics held on each Thursday at MCM110. More info can be found on the website.
