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A criterion to estimate the least common multiple of sequences and asymptotic formulas for (3) arising from recurrence relation
 

Summary: A criterion to estimate the least common multiple of sequences
and asymptotic formulas for (3) arising from recurrence relation
of an elliptic function
Shigeki Akiyama
0. Introduction
In [2], the author studied the asymptotic behavior of the least common multiple of a
sequences {an}
n=1 provided that it satisfies certain axioms (A1) and (A2) (see page 4).
Sequences defined by binary linear recurrence, for example, were handled there. A typical
result was
log |a1a2 an|
log[a1, a2, . . . , an]
= (2) + O(
log n
n
), (1)
where [a1, a2, . . . , an] is the least common multiple of the terms a1, a2, . . . , an and () is the
Riemann zeta function. On the origin of these problems and related works, see [7] [5] [1] [2]
[10]. To prove (1) in [2], the fundamental tool employed was to rewrite the least common
multiple by "an inclusion exclusion principle". This was done in [2] with the essential use

  

Source: Akiyama, Shigeki - Department of Mathematics, Niigata University

 

Collections: Mathematics