On the error-sum function of Pierce expansions

Abstract

We introduce the error-sum function of Pierce expansions. Some basic properties of the error-sum function are analyzed. We also examine the fractal property of the graph of it by calculating the Hausdorff dimension, the box-counting dimension, and the covering dimension of the graph.

arXiv comment31 pages; typos corrected

References in corpus (1)

• Variations on an error sum function for the convergents of some powers of $e$

Cited by in corpus (5)

• Hausdorff dimensions in Pierce expansions
• Exceptional sets to Shallit's law of leap years in Pierce expansions
• Convergence exponent of Pierce expansion digit sequences
• An elementary proof that the set of exceptions to the law of large numbers in Pierce expansions has full Hausdorff dimension
• Continuity of the continued fraction mapping revisited