Wyniki wyszukiwania

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Correction to: "On a positivity property of the Riemann ξ-function" (Acta Arith. 89 (1999), 217-234)

100%

Lagarias J.

Acta Arithmetica

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2005

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tom 116

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nr 3

293-294

2

Zero spacing distributions for differenced L-functions

100%

Lagarias J.

Acta Arithmetica

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2005

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tom 120

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nr 2

159-184

3

On a positivity property of the Riemann ξ-function

100%

Lagarias J.

Acta Arithmetica

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1999

|

tom 89

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nr 3

217-234

4

3x+1 inverse orbit generating functions almost always have natural boundaries

64%

Bell J., Lagarias J.

Acta Arithmetica

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2015

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tom 170

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nr 2

101-120

EN

The 3x+k function $T_{k}(n)$ sends n to (3n+k)/2, resp. n/2, according as n is odd, resp. even, where k ≡ ±1 (mod 6). The map $T_k(·)$ sends integers to integers; for m ≥1 let n → m mean that m is in the forward orbit of n under iteration of $T_k(·)$. We consider the generating functions $f_{k,m}(z) = ∑_{n>0, n → m} z^{n}$, which are holomorphic in the unit disk. We give sufficient conditions on (k,m) for the functions $f_{k,m}(z)$ to have the unit circle {|z|=1} as a natural boundary to analytic continuation. For the 3x+1 function these conditions hold for all m ≥1 to show that $f_{1,m}(z)$ has the unit circle as a natural boundary except possibly for m= 1, 2, 4 and 8. The 3x+1 Conjecture is equivalent to the assertion that $f_{1, m}(z)$ is a rational function of z for the remaining values m = 1,2,4,8.

5

Bounds for the 3x+1 problem using difference inequalities

64%

Krasikov I., Lagarias J.

Acta Arithmetica

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2003

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tom 109

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nr 3

237-258

6

Product-free sets with high density

51%

Kurlberg P., Lagarias J., Pomerance C.

Acta Arithmetica

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2012

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tom 155

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nr 2

163-173

7

On the range of fractional parts {ξ(p/q)ⁿ}

51%

Flatto L., Lagarias J., Pollington A.

Acta Arithmetica

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1995

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tom 70

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nr 2

125-147

Ograniczanie wyników

7 Acta Arithmetica

7 Lagarias J.

1 Bell J.

1 Flatto L.

1 Krasikov I.

1 Kurlberg P.

1 Pollington A.

1 Pomerance C.

1 2015

1 2012

2 2005

1 2003

1 1999

1 1995

Correction to: "On a positivity property of the Riemann ξ-function" (Acta Arith. 89 (1999), 217-234)

Zero spacing distributions for differenced L-functions

On a positivity property of the Riemann ξ-function

3x+1 inverse orbit generating functions almost always have natural boundaries

Bounds for the 3x+1 problem using difference inequalities

Product-free sets with high density

On the range of fractional parts {ξ(p/q)ⁿ}