Some Equations Involving the Gamma Function

TL;DR

This paper proves that the intersection of a certain algebraic variety with the graph of the Gamma function is Zariski dense, revealing deep connections between algebraic geometry and special functions.

Contribution

It establishes the Zariski density of the Gamma function's graph intersecting a broad class of algebraic varieties, advancing understanding of transcendental number theory.

Findings

Zariski density of the Gamma function's graph in certain varieties

Connection between algebraic varieties and special functions

Advancement in transcendental number theory

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 $V$.