Subword complexity and finite characteristic numbers

Firicel, Alina

Actes des rencontres du CIRM, Tome 1 (2009) no. 1, pp. 29-34.

Decimal expansions of classical constants such as $\sqrt{2}$, $\pi$ and $\zeta \left(3\right)$ have long been a source of difficult questions. In the case of finite characteristic numbers (Laurent series with coefficients in a finite field), where no carry-over difficulties appear, the situation seems to be simplified and drastically different. On the other hand, the theory of Drinfeld modules provides analogs of real numbers such as $\pi$, $e$ or $\zeta$ values. Hence, it became reasonable to enquire how “complex” the Laurent representation of these “numbers” is.

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