In:
Nonlinearity, IOP Publishing, Vol. 37, No. 2 ( 2024-02-01), p. 025008-
Abstract:
The study of products of consecutive partial quotients in the continued fraction arises naturally out of the improvements to Dirichlet’s theorem. We study the distribution of the two large products of partial quotients among the first n terms. More precisely, writing [ a 1 ( x ) , a 2 ( x ) , … ] the continued fraction expansion of an irrational number x ∈ ( 0 , 1 ) , for a non-decreasing function φ : N → R , we completely determine the size of the set F 2 ( φ ) = x ∈ [ 0 , 1 ) : ∃ 1 ⩽ k ≠ l ⩽ n , a k ( x ) a k + 1 ( x ) ⩾ φ ( n ) , a l ( x ) a l + 1 ( x ) ⩾ φ ( n ) for infinitely many n ∈ N in terms of Lebesgue measure and Hausdorff dimension.
Type of Medium:
Online Resource
ISSN:
0951-7715
,
1361-6544
DOI:
10.1088/1361-6544/ad140f
Language:
Unknown
Publisher:
IOP Publishing
Publication Date:
2024
detail.hit.zdb_id:
1361512-9
SSG:
17,1
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