The number of S4-fields with given discriminant
Jürgen Klüners · Acta Arithmetica · 2006
Abstract. We prove that the number of S4-extensions of the rationals of given discriminant d is O(d 1/2+ǫ) for all ǫ> 0. For a prime number C we derive that the number of octahedral modular forms of weight 1 and conductor C is bounded above by O(C 1/2 log(C) 2). 1.