Prime-power spectral eigenvalues

Determine whether, for every prime number p, every positive power p^n is a spectral integer eigenvalue of a given spectral pair $(\mu,\Lambda)$.

Background

The question concerns the spectral integer eigenvalue problem for canonical spectral pairs, where the scaling parameter is restricted to positive integers. It asks whether spectrality is preserved along the entire sequence of powers of any prime.

The paper proves this assertion in several important cases, including the fourth middle Cantor measure for primes greater than 3 and certain generalized Cantor measures, but poses the question explicitly as a general problem.

References

Let $p$ be a prime. Is $pn$ a spectral integer eigenvalue for the spectral pair $(\mu, \Lambda)$ for all $n\geq1$?

— Spectral eigenvalue problem of Cantor measures and Artin's primitive root conjecture  (2609.29038 - He et al., 24 Sep 2026) in Question 1, Section 1 (Introduction)