On the sum of digits of 1/M in \mathbbF_q[x]

2021/08/23 by Zeév Rudnick, Rudnick, Zeev
Mathematics · Computer Science · #Analytic Number Theory Research #Algebraic Geometry and Number Theory #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.2108.10142

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 ℚ(√(-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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