turkmath.org

Recently, one of the breakthrough results in mathematics is the proof of the Sato-Tate conjecture by Taylor, Barnet-Lamb, Geraghty and Harris. Let f be a cusp form of weight k + 1/2 and at most quadratic nebentype character whose Fourier coefficients a(n) are all real. Then Bruinier and Kohnen suggested that the a(n)’s are equidistributed. In this talk, we will give some results on the Bruinier-Kohnen sign equidistribution conjecture using the Sato-Tate conjecture which is a theorem now. Furthermore, we will explain current position of the conjecture and conclude with some open problems in theory of automorphic forms.