Fermat's Last Theorem in star-invariant subspaces: capacity-zero boundary spectrum

Stephan Ramon Garcia

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arXiv · 2608.11653

Fermat's Last Theorem in star-invariant subspaces: capacity-zero boundary spectrum

Stephan Ramon Garcia

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Abstract

We prove that the Fermat equation $f^n+g^n=h^n$ with exponent $n\geq 4$ has no nontrivial solutions $f,g,h$ in the star-invariant subspace $K_\theta^p$, in which $1\leq p\leq\infty$, whenever the boundary spectrum of the inner function $\theta$ has logarithmic capacity zero. This gives a positive answer, for this class of inner functions and exponents, to a problem posed by Dyakonov.

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Stephan Ramon Garcia. 2026-08-12. Fermat's Last Theorem in star-invariant subspaces: capacity-zero boundary spectrum. https://arxiv.org/abs/2608.11653

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