Some equations involving the gamma function

Eterović, Sebastian; Padgett, Adele

doi:10.1090/tran/9361

Some equations involving the gamma function
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by Sebastian Eterović and Adele Padgett;

Trans. Amer. Math. Soc.

DOI: https://doi.org/10.1090/tran/9361

Published electronically: January 21, 2025

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Abstract:

Let $V\subseteq \mathbb {C}^{2n}$ be an algebraic variety with no constant coordinates and with a dominant projection onto the first $n$ coordinates. We show that the intersection of $V$ with the graph of the $\Gamma$ function is Zariski dense in $V$. Our method gives an explicit description of the distribution of these intersection points, and can be adapted for some other functions.

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