On the metric theory of nearest integer continued fractions

Riesel, Hans

doi:10.1007/bf01934188

BIT

1987

DOI: 10.1007/bf01934188

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On the metric theory of nearest integer continued fractions

Hans Riesel

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Cited by 3 publications

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“…

The problems empirically studied by the author [1] respectively, where G = (1+x/5)/2. The numerical valu.es given for re(t) are quite accurate; the largest error is 0.64.10-5, occurring for t = 0.14.

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confidence: 99%

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On the metric theory of nearest integer continued fractions

Riesel¹

1988

BIT

Self Cite

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The problems empirically studied by the author [1] respectively, where G = (1+x/5)/2. The numerical valu.es given for re(t) are quite accurate; the largest error is 0.64.10-5, occurring for t = 0.14. The values for m'(t) differ by up to 3 units in the last decimal, except the value for m'(0), which differs by 4 units. The exact value of the constant In K' in (38) and (41) is u2/121n G = 1.709...The ratio 70 ~ at the end ofsubsection 17 is In G/ln 2 = 0.6942... H. Riese••

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“…

The problems empirically studied by the author [1] respectively, where G = (1+x/5)/2. The numerical valu.es given for re(t) are quite accurate; the largest error is 0.64.10-5, occurring for t = 0.14.

…”

mentioning

confidence: 99%

“…The problems empirically studied by the author [1] have earlier been completely solved by Rieger [2], [3] and Rockett [4]. See also [5].…”

mentioning

confidence: 99%

On the metric theory of nearest integer continued fractions

Riesel¹

1988

BIT

Self Cite

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New formulation of the two body problem using a continued fractional potential

El-Salam

El-Bar

Rasem

et al. 2014

Astrophys Space Sci

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Midpoint criteria for solving Pell’s equation using the nearest square continued fraction

Matthews

Robertson²,

White

2010

Math. Comp.

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Abstract. We derive midpoint criteria for solving Pell's equation x 2 − Dy 2 = ±1, using the nearest square continued fraction expansion of √ D. The period of the expansion is on average 70% that of the regular continued fraction. We derive similar criteria for the diophantine equation y 2 = ±1, where D ≡ 1 (mod 4). We also present some numerical results and conclude with a comparison of the computational performance of the regular, nearest square and nearest integer continued fraction algorithms.

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On the metric theory of nearest integer continued fractions

Cited by 3 publications

References 3 publications

On the metric theory of nearest integer continued fractions

On the metric theory of nearest integer continued fractions

New formulation of the two body problem using a continued fractional potential

Midpoint criteria for solving Pell’s equation using the nearest square continued fraction

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