TY - JOUR
AB - We prove that the number of quartic S4--extensions of the rationals of given discriminant d is $O_\eps(d^{1/2+\eps})$ for all $\eps>0$. For a prime number p we derive that the dimension of the space of octahedral modular forms of weight 1 and conductor p or p² is bounded above by O(p¹/²log(p)²).
AU - Klüners, Jürgen
ID - 34892
IS - 2
JF - Acta Arithmetica
KW - Algebra and Number Theory
SN - 0065-1036
TI - The number of S₄-fields with given discriminant
VL - 122
ER -