The Constant κH: Definition, Arithmetic Properties, and Its Relation to C (Paper 19 of the LQG–LQC Intertwiner Series)
Year: 2026
Type: preprint
Abstract: IntroductionThe constant C = 3.60329350391382... — studied in depth in Paper 8 [3] — is the maximumvalue of the LQC bounce window function. Paper 8 established its Gamma-function representation, irrationality, and conditional transcendence, and introduced the family C(λ). The present paper gives the same systematic treatment to the companion constant κH =3.44162326276297..., the location at which the maximum occurs. This constant was referred to as κmax in all prior papers of this series (Papers 1–18). Here we treat it systematically as an object of independent interest.
Author: S.E., Hillard
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203864916
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