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PARAMETRIC GEOMETRY OF NUMBERS IN FUNCTION FIELDS

  • Damien Roy (a1) and Michel Waldschmidt (a2)

Abstract

We transpose the parametric geometry of numbers, recently created by Schmidt and Summerer, to fields of rational functions in one variable and analyze, in that context, the problem of simultaneous approximation to exponential functions.

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1. Baker, A., On an analogue of Littlewood’s Diophantine approximation problem. Michigan Math. J. 11 1964, 247250.
2. Hermite, Ch., Sur la fonction exponentielle. C. R. Acad. Sci. Paris 77 1873, 1824 74–79, 226–233, 285–293; Œuvres de Charles Hermite, Vol. 3, 150–181.
3. Hermite, Ch., Sur la généralisation des fractions continues algébriques (extrait d’une lettre à M Pincherle). Ann. Mat. 21 1893, 289308; Œuvres de Charles Hermite, Vol. 4, 357–377.
4. Jager, H., A multidimensional generalization of the Padé table I–VI. Nederl. Akad. Wet. Proc. Ser. A 67 1964, 193249.
5. Keita, A., Continued fractions and parametric geometry of numbers. J. Théor. Nombres Bordeaux 29 2017, 129135.
6. Mahler, K., Zur Approximation der Exponentialfunktion und des Logarithmus I. J. Reine Angew. Math. 166 1931, 118136.
7. Mahler, K., An analogue to Minkowski’s geometry of numbers in a field of series. Ann. of Math. (2) 42 1941, 488522.
8. Mahler, K., On compound convex bodies I, II. Proc. Lond. Math. Soc. (3) 5 1955, 358384.
9. Mahler, K., Perfect systems. Compos. Math. 19 1968, 95166.
10. Roy, D., On Schmidt and Summerer parametric geometry of numbers. Ann. of Math. (2) 182 2015, 739786.
11. Schmidt, W. M., Open problems in Diophantine approximations. In Approximations diophantiennes et nombres transcendants (Luminy, 1982) (Progress in Mathematics 31 ), Birkhäuser (Boston, MA, 1983), 271287.
12. Schmidt, W. M. and Summerer, L., Parametric geometry of numbers and applications. Acta Arith. 140 2009, 6791.
13. Schmidt, W. M. and Summerer, L., Diophantine approximation and parametric geometry of numbers. Monatsh. Math. 169 2013, 51104.
14. Thunder, J. L., Siegel’s lemma for function fields. Michigan Math. J. 42 1995, 147162.
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