Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms
Let l and m be two integers with l > m ≥ 0, and let a and b be integers with a ≥ 1 and a + b ≥ 1. In this paper, we prove that log lcm mn < i ≤ ln { ai + b } = An + o ( n ), where A is a constant depending on l , m and a .
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| Veröffentlicht in: | Archiv der Mathematik 2013-04, Vol.100 (4), p.337-345 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
l
and
m
be two integers with
l
>
m
≥ 0, and let
a
and
b
be integers with
a
≥ 1 and
a
+
b
≥ 1. In this paper, we prove that log lcm
mn
<
i
≤
ln
{
ai
+
b
} =
An
+
o
(
n
), where
A
is a constant depending on
l
,
m
and
a
. |
|---|---|
| ISSN: | 0003-889X 1420-8938 |
| DOI: | 10.1007/s00013-013-0510-7 |