Moments of non-normal number fields -- II

Abstract

Suppose $K$ is a number field and $a_K(m)$ is the number of integral ideals of norm equal to $m$ in $K$, then for any integer $l$, we asymptotically evaluate the sum \[ \sum_{m\leqslant T} a_K^l(m) \] as $T\to \infty$. We also consider the moments of the corresponding Dedekind zeta function. We prove lower bounds of expected order of magnitude and slightly improve the known upper bound for the second moment in the non-Galois case.

Slightly modified exposition, provided more details in some proofs, 13 pages, comments welcome

References in corpus (1)

• On Moments of non-normal number fields