The Takagi function: a survey

Details The Takagi function: a survey The Takagi function: a survey

2011-10-08

arxiv.org/abs/1110.1691v2

Mathematics

Classical Analysis and ODEs

52 pages, 6 figures

Scientific paper

This paper sketches the history of the Takagi function T and surveys known properties of T, including its nowhere-differentiability, modulus of continuity, graphical properties and level sets. Several generalizations of the Takagi function, in as far as they are based on the "tent map", are also discussed. The final section reviews a number of applications of the Takagi function to various areas of mathematics, including number theory, combinatorics and classical real analysis.

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