Continued fractions for quadratic elements in formal power series |
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Authors: | Jun-Ichi Tamura Shin-Ichi Yasutomi |
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Affiliation: | (1) Nagoya University, Nagoya, Japan; |
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Abstract: | There exist certain quadratic elements α∈?((t ?1)) over the rational function field ?(t) having nonperiodic continued fraction expansion, see W.M. Schmidt in (Acta Arith. 95(2):139–166, 2000). Hence we need a modification of Lagrange’s theorem with regard to function fields instead of number fields. In this paper, we introduce a class of continued fractions and describe Lagrange’s theorem as a conjecture related to quadratic elements over ?(t). We give some examples which support our conjecture. |
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