Quadratic fields with cyclic 2-class groups

TextFor any integer k⩾1k⩾1, we show that there are infinitely many complex quadratic fields whose 2-class groups are cyclic of order 2k2k. The proof combines the circle method with an algebraic criterion for a complex quadratic ideal class to be a square.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=H49W8Wyl47o.