论文信息 - Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations with restricted denominators

Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations with restricted denominators

We consider metric results for the asymptotic behavior of the number of solutions of Diophantine approximation inequalities with restricted denominators for Laurent formal power series with coefficients in a finite field. We especially consider approximations by rational functions whose denominators are powers of irreducible polynomials, and study the strong law of large numbers for the number of solutions of the inequalities under consideration.

[1] Michael Rosen,et al. A classical introduction to modern number theory , 1982, Graduate texts in mathematics.

[2] H. Nakada,et al. Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations , 2006 .

[3] Glyn Harman,et al. Metric number theory , 1998 .

[4] Walter Philipp,et al. Some metrical theorems in number theory , 1967 .

[5] Eveyth Deligero,et al. On the Central Limit Theorem for Non-Archimedean Diophantine Approximations , 2005 .

[6] Wolfgang M. Schmidt,et al. A Metrical Theorem in Diophantine Approximation , 1960, Canadian Journal of Mathematics.

[7] R. Odoni. A CLASSICAL INTRODUCTION TO MODERN NUMBER THEORY (Graduate Texts in Mathematics, 84) , 1984 .

[8] V. G. Sprindzhuk. Metric theory of diophantine approximations , 1979 .

[9] Michael Fuchs,et al. On Metric Diophantine Approximation in the Field of Formal Laurent Series , 2002 .

[10] Harald Niederreiter,et al. Kronecker-type sequences and nonarchimedean diophantine approximations , 1993 .

[11] Michael Fuchs,et al. Invariance principles for Diophantine approximation of formal Laurent series over a finite base field , 2007, Finite Fields Their Appl..

[12] Hitoshi Nakada,et al. On metric Diophantine approximation in positive characteristic , 2003 .