On hybrid moments of Δ2(x) and Δ3(x)
Let k ⩾ 2 be a fixed natural number and d k ( n ) denote the number of ways n can be written as a product of k positive integers. We use Δ k ( x ) to denote the error term in the asymptotic formula of the summatory function of d k ( n ) . The aim of this paper is to study the hybrid moments of Δ 2 (...
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| Veröffentlicht in: | The Ramanujan journal 2022, Vol.58 (2), p.597-631 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
k
⩾
2
be a fixed natural number and
d
k
(
n
)
denote the number of ways
n
can be written as a product of
k
positive integers. We use
Δ
k
(
x
)
to denote the error term in the asymptotic formula of the summatory function of
d
k
(
n
)
.
The aim of this paper is to study the hybrid moments of
Δ
2
(
x
)
and
Δ
3
(
x
)
. The higher power moments of
Δ
2
(
x
)
are also studied. |
|---|---|
| ISSN: | 1382-4090 1572-9303 |
| DOI: | 10.1007/s11139-021-00431-w |