What question did this study set out to answer?

The aim is to establish a representation for the pcf-delta growth constant using Fredholm determinants and to analyze its properties including order and genus.

June 12, 2026Open Access

A Fredholm-determinant representation of the pcf-delta growth constant: finite identity, entire order and genus

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The aim is to establish a representation for the pcf-delta growth constant using Fredholm determinants and to analyze its properties including order and genus.
Defined u_n using a positive quadratic b(k) and analyzed its contributions to the growth constant.
Applied the Fredholm-determinant representation delta = (1/2) log det(I + T^2) with edge-weighted path operator T.
Conducted numerical confirmations and theoretical derivations including a study of the entire order and genus of the weighted independence polynomial.
Confirmed the Fredholm representation numerically to 65 significant digits across two independent methods.
Determined the entire order of R_inf as rho = 1/4 and its genus as 0 based on Hadamard product analysis.
Established bounds for the trace-class convergence of the series S, revealing specific conditions under which S < 1.

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Implication

Note reveals the Fredholm-determinant representation of the pcf-delta growth constant, highlighting its mathematical implications.

Cite This Study

Papanokechi (2026) studied this question.

synapsesocial.com/papers/6a2ba5068101cf8926f03483 https://doi.org/10.5281/zenodo.20624813

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A Fredholm-determinant representation of the pcf-delta growth constant: finite identity, entire order and genus

Key Points

Discussion

Implication

Cite This Study

A Fredholm-determinant representation of the pcf-delta growth constant: finite identity, entire order and genus

Key Points

Discussion

Implication

Cite This Study

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