Characterization of equality points for the modulus of continuity

Characterize explicitly the set of δ∈[0,1/2] for which the modulus of continuity max_{0≤h≤δ}T(h) of the base-3 Delange function equals T(δ).

Background

The paper studies the modulus of continuity of the base-3 Delange function T, namely max_{0≤h≤δ}T(h), and identifies an infinite family of points δ=1/(2·3a) where this modulus equals T(δ). It also gives an example, δ=1/3, where the modulus is strictly larger than T(δ), leaving the complete set of equality points unknown.

References

We do not know an explicit description of the set of $\delta\in[0,1/2]$ at which it equals $T(\delta)$.

— Local Extrema and Infinite Derivatives of the Delange Function of Base 3  (2610.21265 - Zhu, 15 Oct 2026) in Section “Other bases and further questions”