Jeffrey C. Lagarias: 3x+1 problem and related problems


  • The 3x+1 problem and its generalizations ,
    Jeffrey C. Lagarias,
    Amer. Math. Monthly 92 (1985) 3-23.
    [Reprinted in: Conference on Organic Mathematics,
    Canadian Math. Society Conference Proceedings vol 20, 1997, pp. 305-331]
    This paper is on the Web at: www.cecm.sfu.ca/organics/papers

  • The 3x+1 Problem: An Annotated Bibliography (1963-1999) (sorted by author) ,
    Jeffrey C. Lagarias,
    Unpublished .
    preprint on arXiv [arxiv.org/abs/math/0309224]

  • The 3x+1 Problem: An Annotated Bibliography, II (2000-2009) ,
    Jeffrey C. Lagarias,
    Unpublished .
    preprint on arXiv [arxi.org/abs/math/0608208]

  • The set of rational cycles for the 3x+1 problem ,
    J. C. Lagarias,
    Acta Arithmetica 56 (1990), pp. 33-53.

  • The 3x+1 Problem: Two Stochastic Models ,
    Jeffrey C. Lagarias and Alan Weiss,
    Annals of Applied Probability 2 (1992), pp. 229-261.

  • Density Bounds for the 3x+1 Problem I. Tree-Search Method ,
    David Applegate and Jeffrey C. Lagarias,
    Math. Comp. 64 (1995), pp. 411-426.

  • Density Bounds for the 3x+1 Problem II. Krasikov Inequalities .
    David Applegate and Jeffrey C. Lagarias,
    Math. Comp. 64 (1995), pp. 427-438.

  • The Distribution of 3x+1 Trees ,
    David Applegate and Jeffrey C. Lagarias,
    Experimental Math. 4 (1995), pp. 193-209.

  • The 3x+1 Conjugacy Map ,
    Daniel J. Bernstein and Jeffrey C. Lagarias,
    Canadian J. Math. 48 (1996), pp. 1154-1169. [PostScript] [Pdf]

  • Lower bounds for the total stopping time of 3x+1 iterates ,
    D. Applegate and J. C. Lagarias,
    Math. Comp. 72 (2003), 1035--1049 .
    preprint on arXiv . [arxiv.org/abs/math/0103054]

  • Bounds for the 3x+1 problem using difference inequalities ,
    Ilia Krasikov and J. C. Lagarias,
    Acta Arithmetica 109 (2003), No. 3, 237--258 .
    preprint on arXiv . [arxiv.org/abs/math/0205002]

  • Approximate Squaring ,
    J. C. Lagarias and N. J. A. Sloane,
    Experimental Math. 13 (2004), 113-128
    preprint on arXiv . [arxiv.org/abs/math/0309389]

  • Wild and Wooley numbers ,
    Jeffrey C. Lagarias
    Amer. Math. Monthly 113 (2006), 97--108.
    preprint on arXiv [arxiv.org/abs/math/0411141].

  • The 3x+1 semigroup ,
    David Applegate and Jeffrey C. Lagarias
    J. Number Theory, 117 (2006), 146--159.
    preprint on arXiv [arxiv.org/abs/math/0411140].

  • Benford's law for the 3x+1 function ,
    Jeffrey C. Lagarias and K. Soundararajan
    J. London Math. Soc, 74 (2006), 289--303.
    preprint on arXiv [arxiv.org/abs/math/0509175].

  • Stochastic models for the 3x+1 and 5x+1 functions ,
    Alex V. Kontorovich and Jeffrey C. Lagarias
    in: The Ultimate Challenge: The 3x+1 problem, Amer. Math. Soc.: Providence RI 2010, pp. 131--188
    preprint on arXiv [arXiv:0910.1944].


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