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Riemannova funkcia je matematická funkcia, ktorá je obdobou Dirichletovej funkcie. Ide o reálnu funkciu reálnej premennej definovanú nasledujúcim vzťahom:
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![{\displaystyle f(x)={\begin{cases}{\frac {1}{q}}&x={\frac {p}{q}}\in [0,1]\cap \mathbb {Q} \ ,{\mbox{kde }}{\frac {p}{q}}\ {\mbox{je }}{\mbox{zakladny }}{\mbox{tvar }}{\mbox{racionalneho }}{\mbox{cisla }}x\\0&x\in [0,1]\setminus \mathbb {Q} \end{cases}}}](http://wikimedia.org/api/rest_v1/media/math/render/svg/de654bb64ecadf7e8ed5168e2b342074cadd25f4)
