On the sum of digits of $1/M$ in $\mathbb{F}_q[x]$

Zeev Rudnick

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arXiv · 2108.10142

On the sum of digits of $1/M$ in $\mathbb{F}_q[x]$

Zeev Rudnick

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Abstract

For certain primes $p$, the average digit in the expansion of $1/p$ was found to have a deviation from random behaviour related to the class number of the imaginary quadratic field $\mathbb{Q}(\sqrt{-p})$ (Girstmair 1994). In this short note, we observe that for the corresponding problem when we replace the integers by polynomials over a finite field, there is never any bias. The argument is elementary.

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Zeev Rudnick. 2021-08-23. On the sum of digits of $1/M$ in $\mathbb{F}_q[x]$. https://arxiv.org/abs/2108.10142

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