| Abstract: |
| The differentiability of the one parameter family of Okomoto`s functions as functions of $x$ has been analyzed extensively since their introduction in 2005. In this talk, we motivate why one might choose to study the partial derivative with respect to the parameter before then considering this partial derivative for Okomoto`s functions. We place a significant focus on $a = 1/3$ as an analogue to our motivation and describe the properties of a nowhere differentiable function derived from this setting, $K(x)$, for which the set of points of infinite derivative produces an example of a measure zero set with Hausdorff dimension $1$. Time allowing, we will look to future questions stemming from this work. |
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