Folds! II: Symmetry disturbed. (English) Zbl 0493.10002

See the joint review of all three parts in Zbl 0493.10001.
Reviewer: F. Beukers


11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11J81 Transcendence (general theory)
68Q45 Formal languages and automata
11A55 Continued fractions
Full Text: DOI


[1] A. Blanchard, M. Mendès France: Symétrie et Trans-cendance.Bull. Sci. Math. 106 (1982)
[2] W. A. Beyer, N. Metropolis, J. R. Neergard: Statistical study of the digits of some square roots of integers in various bases.Math. Comp. 24 (1970), 455–473 For references to further statistical studies of the digits of irrational numbers, see L. Kuipers and H. Niederreiter:Uniform distribution of sequences (Wiley, 1974) · Zbl 0208.19505
[3] G. Christol, T. Kamae, M. Mendès France, G. Rauzy: Suites algébriques, automates et substitutions.Bull. Soc. Math. France 108 (1980), 401–419 · Zbl 0472.10035
[4] A. Cobham: Uniform tag sequences,Math. Systems Theory 6 (1972), 164–192. Also: On the Hartmanis-Stearns problem for a class of tag machines,Technical Report RC2178 (1968) IBM Research Centre, York-town Heights, N.Y., and: On the base dependence of sets of numbers recognisable by finite automata.Math. Systems Theory 3 (1969), 186-192 · Zbl 0253.02029
[5] Chandler Davis, Donald E. Knuth: Number representations and dragon curves I.J. Recreational Math. 3 (1970) 61–81; II 3 (1970), 133-149
[6] F. M. Dekking, M. Mendès France: Uniform distribution modulo one: a geometrical viewpoint.J. Reine Angew. Math. (Crelle) 329 (1981), 143–153 · Zbl 0459.10025
[7] Sir Alan Gardiner:Egyptian Grammar (Oxford University Press, 3rd edn. 1964)
[8] M. Henon, Y. Pomeau: Two strange attractors with simple structure, in:Turbulence and Navier-Stokes equation. Springer, Lecture Notes in Mathematics 565 (1976), 29–68
[9] M. Kmošek: Report by A. Schinzel, Oberwolfach (28 May–2 June, 1979)
[10] J. H. Loxton, A. J. van der Poorten: Arithmetic properties of certain functions in several variables III.Bull. Austral. Math. Soc. 16 (1977), 15–47 · Zbl 0339.10028
[11] J. H. Loxton, A. J. van der Poorten: Transcendence and algebraic independence by a method of Mahler.Transcendence theory: advances and applications, A. Baker, D. W. Masser, eds (Academic Press, 1977), 211–226 · Zbl 0378.10020
[12] J. H. Loxton, A. J. van der Poorten: Arithmetic properties of the solutions of a class of functional equations.J. Reine Angew. Math. (Crelle) 330 (1982), 159–172 · Zbl 0468.10019
[13] M. Mendès France: Entropy of curves and uniform distribution, Proc. Colloquia Mathematicae Societatis Jânos Bolyai · Zbl 0547.10047
[14] M. Mendès France, A. J. van der Poorten: Arithmetic and analytic properties of paperfolding sequences (dedicated to Kurt Mahler).Bull. Austral. Math. Soc. 24 (1981), 123–131 · Zbl 0451.10018
[15] A. J. van der Poorten: Substitution automata, functional equations and functions ”algebraic over a finite field”Contemporary Math. 9 (1982), 307–312 · Zbl 0493.10039
[16] A. Pethö: Some continued fraction expansions for the Fredholm numbers.J. Number Theory 14 (1982), 232–236 · Zbl 0481.10006
[17] G. Polya, G. Szegö:Problems and Theorems in Analysis I, II (Springer 1976). Translation of ”Aufgabenund Lehrsätze aus der Analysis I, II.”
[18] Luis A. Santaló:Integral geometry and geometric probability, Encyclopaedia of Math. and its Applications, Vol. 1 (Addison-Wesley, 1976)
[19] J. Shallit: Simple continued fractions for some irrational numbers,J. Number Theory 11 (1979), 209–217 Also: Continued fractions for Liouville’s numbers {\(\Sigma\)}e -k! ; Explicit description of some continued fractions,Fibonacci Quart.; Simple continued fractions for some irrational numbers II · Zbl 0404.10003
[20] G. Köhler: Some more predictable continued fractions.Monatsh. Math. 89 (1980), 95–100 · Zbl 0419.10010
[21] H. J. S. Smith: De compositione numerorum primorum formae 4{\(\lambda\)} + 1 ex duobus quadratis.J. Reine Angew. Math. (Crelle) 50 (1855), 91–92 · ERAM 050.1326cj
[22] E. A. Wallis-Budge: transl.The Book of the Dead (University Books, NY 1960)
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