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arXiv · 2509.24982

Bialgebraic varieties of the Gamma function

Sebastian Eterović·Adele Padgett·Roy Zhao
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Abstract

We characterize the bialgebraic varieties of the $\Gamma$ function, that is, if $V,W\subseteq\mathbb{C}^n$ are irreducible affine algebraic variety which satisfy $\dim V =\dim W$ and $\Gamma(V)\subseteq W$, then the equations defining $V$ (and hence also $W$) either give an equality between coordinates, or set some coordinates to be constant. We also classify the case where $V$ and $W$ have the same dimension as varieties over the field of algebraic functions.

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Sebastian Eterović, Adele Padgett, Roy Zhao. 2025-09-29. Bialgebraic varieties of the Gamma function. https://arxiv.org/abs/2509.24982

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