Moments of non-normal number fields -- II
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917895738490880 |
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| author | Krishnamoorthy, Krishnarjun |
| author_facet | Krishnamoorthy, Krishnarjun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09768 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Moments of non-normal number fields -- II Krishnamoorthy, Krishnarjun Number Theory 11F66, 11F30, 11R42, 20C30 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. |
| title | Moments of non-normal number fields -- II |
| topic | Number Theory 11F66, 11F30, 11R42, 20C30 |
| url | https://arxiv.org/abs/2310.09768 |