TY - JOUR

T1 - On metric diophantine approximation in the field of formal Laurent series

AU - Fuchs, Michael

PY - 2002/1/1

Y1 - 2002/1/1

N2 - B. deMathan (1970, Bull. Soc. Math. France Supl. Mem. 21) proved that Khintchine's Theorem has an analogue in the field of formal Laurent series. First, we show that in case of only one inequality this result can also be obtained by continued fraction theory. Then, we are interested in the number of solutions and show under special assumptions that one gets a central limit theorem, a law of iterated logarithm and an asymptotic formula. This is an analogue of a result due to W. J. LeVeque (1958, Trans. Amer. Math. Soc. 87, 237-260). The proof is based on probabilistic results for formal Laurent series due to H. Niederreiter (1988, in Lecture Notes in Computer Science, Vol. 330, pp. 191-209, Springer-Verlag, New York/Berlin).

AB - B. deMathan (1970, Bull. Soc. Math. France Supl. Mem. 21) proved that Khintchine's Theorem has an analogue in the field of formal Laurent series. First, we show that in case of only one inequality this result can also be obtained by continued fraction theory. Then, we are interested in the number of solutions and show under special assumptions that one gets a central limit theorem, a law of iterated logarithm and an asymptotic formula. This is an analogue of a result due to W. J. LeVeque (1958, Trans. Amer. Math. Soc. 87, 237-260). The proof is based on probabilistic results for formal Laurent series due to H. Niederreiter (1988, in Lecture Notes in Computer Science, Vol. 330, pp. 191-209, Springer-Verlag, New York/Berlin).

KW - Continued fractions

KW - Finite fields

KW - Formal Laurent series

KW - Metric diophantine approximation

UR - http://www.scopus.com/inward/record.url?scp=0036639621&partnerID=8YFLogxK

U2 - 10.1006/ffta.2001.0346

DO - 10.1006/ffta.2001.0346

M3 - Article

AN - SCOPUS:0036639621

VL - 8

SP - 343

EP - 368

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

SN - 1071-5797

IS - 3

ER -