Introduction

Abstract

Let ×⁽¹²⁾ be the unique even non-trivial Dirichlet character mod 12, and let ×⁽⁴⁾ be the unique (odd) non-trivial Dirichlet character mod 4. Consider on the line the distributions

$$ \begin{gathered} \mathfrak{d}_{even} \left( x \right) = \sum\limits_{m \in \mathbb{Z}} {\chi ^{\left( {12} \right)} \left( m \right)\delta \left( {x - \frac{m} {{\sqrt {12} }}} \right),} \hfill \\ \mathfrak{d}_{odd} \left( x \right) = \sum\limits_{m \in \mathbb{Z}} {\chi ^{\left( 4 \right)} \left( m \right)\delta \left( {x - \frac{m} {2}} \right).} \hfill \\ \end{gathered} $$

((1.1))