On the distribution of integral ideals and Hecke Grössencharacters (Q606353)

The author proves that for any number field of degree \(n\) over \({\mathbb Q}\) we have that \[ A(x)=cx+O(x^{1-\frac{3}{n+6}+\varepsilon}) \] and \[ B(x)\ll x^{1-\frac{3}{n+6}+\varepsilon}, \] where \(A(x)\) is the number of integral ideals with norm \(\leq x\), \(c\) is the classical constant, and \[ B(x)=\sum_{N({\mathfrak a})\leq x}\lambda({\mathfrak a}), \] \(\lambda\) a Hecke Grössencharacter.