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This work aims to propose a transcendence predicate based on the balanced discriminant of degree-two polynomial continued fractions.

June 1, 2026Open Access

Complex Multiplication as a Transcendence Predicate for Degree-2 Polynomial Continued Fractions

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This work aims to propose a transcendence predicate based on the balanced discriminant of degree-two polynomial continued fractions.
The study investigates the PSLQ detectability of 30 degree-two families based on their discriminants.
Employs the Spectral classification framework and adds components to fix cross-paper inconsistencies.
Conducted empirical tests using specific recurrence-parameter channels and Borel-resummation channels.
24 families show PSLQ-detectability against a basis, suggesting a positive signal for transcendence.
6 candidates demonstrate PSLQ non-detection, indicating challenges in establishing closed forms.
The V_quad family is confirmed as a non-classical Painleve V transcendent, expanding the understanding of its structure.

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Randomized trial examines transcendence predicate effectiveness in polynomial continued fractions, highlighting significant findings.

papanokechi papanokechi (2026) studied this question.

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