  We consider the upper bound of Piltz divisor problem over number fields.
Piltz divisor problem is known as a generalization of the Dirichlet divisor
problem. We deal with this problem over number fields and improve the error
term of this function for many cases. Our proof uses the estimate of
exponential sums. We also show uniform results for ideal counting function and
relatively $r$-prime lattice points as one of applications.
