A certain character twisted average value of the digits of rational numbers and the class numbers of imaginary quadratic fields

ACTA ARITHMETICA（2023）

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Abstract

We give a closed formula for a certain character twisted average value of the digits of the base $g$ expansion of $a/m$ ($2\leq m\in \mathbb N$, $a \in \mathbb N$, $1\leq a \lt m$, $(a,m)=1$). The closed formula involves the first generalized Bernoulli nu

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Key words

digits,class numbers,imaginary quadratic fields,Dirichlet characters

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