Local maxima of even-base Delange functions

Determine which points are local maxima of the Delange function D_q for every even integer base q≥4.

Background

The paper extends its classification of local maxima from the base-3 Delange function to Delange functions D_q in every odd base q. For even bases q≥4, the authors note an analogy with Takagi’s function, where local maxima are known to be non-strict, but do not provide a classification of the local maxima themselves.

References

If q\ge4 is even, we expect that no local maximum of D_q is strict, as for Takagi's functionProposition~4.4, but we do not know which points are local maxima.

— 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”