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1
Content available remote

Metric inhomogeneous Diophantine approximation on the field of formal Laurent series

100%
Kim D., Nakada H.
Acta Arithmetica
|
2011
|
tom 150
|
nr 2
129-142
2
Content available remote

Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations

100%
Nakada H., Natsui R.
Acta Arithmetica
|
2006
|
tom 125
|
nr 3
203-214
3
Content available remote

On metric Diophantine approximation in positive characteristic

100%
Inoue K., Nakada H.
Acta Arithmetica
|
2003
|
tom 110
|
nr 3
205-218
4
Content available remote

Mod 2 normal numbers and skew products

81%
Choe G., Hamachi T., Nakada H.
Studia Mathematica
|
2004
|
tom 165
|
nr 1
53-60
EN
Let E be an interval in the unit interval [0,1). For each x ∈ [0,1) define dₙ(x) ∈ {0,1} by $dₙ(x) := ∑_{i=1}^{n} 1_{E} ({2^{i-1}x}) (mod 2)$, where t is the fractional part of t. Then x is called a normal number mod 2 with respect to E if $N^{-1} ∑_{n=1}^{N} dₙ(x)$ converges to 1/2. It is shown that for any interval E ≠(1/6, 5/6) a.e. x is a normal number mod 2 with respect to E. For E = (1/6, 5/6) it is proved that $N^{-1} ∑_{n=1}^{N} dₙ(x)$ converges a.e. and the limit equals 1/3 or 2/3 depending on x.
5
Content available remote

Semisimple extensions of irrational rotations

81%
Lemańczyk M., Mentzen M., Nakada H.
Studia Mathematica
|
2003
|
tom 156
|
nr 1
31-57
EN
We show that semisimple actions of l.c.s.c. Abelian groups and cocycles with values in such groups can be used to build new examples of semisimple automorphisms (ℤ-actions) which are relatively weakly mixing extensions of irrational rotations.
6
Content available remote

Metric and arithmetic properties of mediant-Rosen maps

81%
Kraaikamp C., Nakada H., Schmidt T.
Acta Arithmetica
|
2009
|
tom 137
|
nr 4
295-324
7
Content available remote

On metrical theory of diophantine approximation over imaginary quadratic field

70%
Nakada H.
Acta Arithmetica
|
1988
|
tom 51
|
nr 4
393-403
8
Content available remote

The metrical theory of complex continued fractions

50%
Nakada H.
Acta Arithmetica
|
1990
|
tom 56
|
nr 4
279-289
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