TL;DR
This paper introduces the beta function of a knot in three-dimensional space, proving it is a meromorphic function satisfying a Bernstein type functional equation and calculating its first residues.
Contribution
It defines a new knot invariant called the beta function, establishing its functional equation and residue properties, advancing knot theory and complex analysis.
Findings
Beta function is meromorphic for knots in 3D space
Satisfies a Bernstein type functional equation
First residues are explicitly determined
Abstract
We introduce the beta function of a knot in euclidean three-space. This is a meromorphic function of a complex variable which we prove admits a Bernstein type functional equation. We determine the first residues.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows