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

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
x0. Introduction
In [2], the author studied the asymptotic behavior of the least common
multiple of a sequences fa n g 1
n=1 provided that it satis es certain axioms
(A1) and (A2) (see page 4). Sequences de ned by binary linear recurrence,
for example, were handled there. A typical result was
log ja 1 a 2       a n j
log[a 1 ; a 2 ; : : : ; a n ]
= (2) +O( log n
n
); (1)
where [a 1 ; a 2 ; : : : ; a n ] is the least common multiple of the terms a 1 ; a 2 ; : : : ; a n
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 exclu-
sion principle". This was done in [2] with the essential use of the axioms

  

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

 

Collections: Mathematics