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Mixing and linear equations over groups in positive characteristic

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Abstract

We prove a result on linear equations over multiplicative groups in positive characteristic. This is applied to settle a conjecture about higher order mixing properties of algebraicZ d-actions.

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References

  • [BM] W. D. Brownawell and D. W. Masser,Vanishing sums in function fields, Mathematical Proceedings of the Cambridge Philosophical Society100 (1986), 427–434.

    MATH  MathSciNet  Google Scholar 

  • [EW] M. Einsiedler and T. Ward,Asymptotic geometry of non-mixing sequences, Ergodic Theory and Dynamical Systems23 (2003), 75–85.

    Article  MATH  MathSciNet  Google Scholar 

  • [E] J.-H. Evertse,On sums of S-units and linear recurrences, Compositio Mathematica53 (1984), 225–244.

    MATH  MathSciNet  Google Scholar 

  • [ESS] J.-H. Evertse, H. P. Schlickewei and W. M. Schmidt,Linear equations in variables which lie in a multiplicative group, Annals of Mathematics155 (2002), 807–836.

    MATH  MathSciNet  Google Scholar 

  • [KS] B. Kitchens and K. Schmidt,Mixing sets and relative entropies for higher-dimensional markov shifts, Ergodic Theory and Dynamical Systems13 (1993), 705–735.

    MATH  MathSciNet  Google Scholar 

  • [L1] S. Lang,Introduction to Algebraic Geometry, Addison-Wesley, Redwood City, CA, 1973.

    Google Scholar 

  • [L2] S. Lang,Fundamentals of Diophantine Geometry, Springer, Berlin, 1983.

    MATH  Google Scholar 

  • [Maso] R. C. Mason,Diophantine Equations over Function Fields, Cambridge University Press, 1984.

  • [Mass] D. W. Masser,Multiplicative isogeny estimates, Journal of the Australian Mathematical SocietyA64 (1998), 178–194.

    Article  MathSciNet  Google Scholar 

  • [N] J. Noguchi,Nevanlinna-Cartan theory over function fields and a Diophantine equation, Journal für die reine und angewandte Mathematik487 (1997), 61–83.

    Article  MATH  MathSciNet  Google Scholar 

  • [PS] A. J. van der Poorten and H. P. Schlickewei,Additive relations in fields, Journal of the Australian Mathematical Society A51 (1991), 154–170.

    MATH  Google Scholar 

  • [S1] K. Schmidt,Dynamical Systems of Algebraic Origin, Birkhäuser, Basel, 1995.

    MATH  Google Scholar 

  • [S2] K. Schmidt,The dynamics of algebraic Z d-actions, inEuropean Congress of Mathematics, Vol. I (Barcelona, 2000), Progress in Mathematics 201, Birkhäuser, Basel, 2001, pp. 543–553.

    Google Scholar 

  • [SW] K. Schmidt and T. Ward,Mixing automorphisms of compact groups and a theorem of Schlickewei, Inventiones Mathematicae111 (1993), 69–76.

    Article  MATH  MathSciNet  Google Scholar 

  • [Sh] I. R. Shafarevich,Basic Algebraic Geometry, Springer, Berlin, 1974.

    MATH  Google Scholar 

  • [SS] H. N. Shapiro and G. H. Sparer,Extension of a theorem of Mason, Communications on Pure and Applied Mathematics47 (1994), 711–718.

    Article  MATH  MathSciNet  Google Scholar 

  • [V1] J. F. Voloch,Diagonal equations over function fields, Boletim da Sociedade Brasileira de Matemática16 (1985), 29–39.

    Article  MATH  MathSciNet  Google Scholar 

  • [V2] J. F. Voloch,The equation ax+by=1 in characteristic p, Journal of Number Theory73 (1998), 195–200.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051, Basel, Switzerland

    D. W. Masser

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  1. D. W. Masser
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Correspondence to D. W. Masser.

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Masser, D.W. Mixing and linear equations over groups in positive characteristic. Isr. J. Math. 142, 189–204 (2004). https://doi.org/10.1007/BF02771532

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  • DOI: https://doi.org/10.1007/BF02771532

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