Randomized trial finds connections in folded-lambda realizations and cusp detection in modular forms, highlighting algebraic independence.
Key Points
The study aims to explore the injective realization of folded-lambda extensions within the context of modular forms and cusp detection.
Constructed linear folded-lambda realizations from M_k(SL_2(Z); C).
Analyzed the differential Galois group in relation to symmetric powers and cuspidal directions.
Examined the regularized Eichler class and established injectivity of the realization.
The linear realization is injective, indicating strong foundational links in modular forms.
All positive even symmetric powers share the same projective Legendre Picard-Vessiot field, showing algebraic independence of scalar cyclic jets.
Cusp detection reveals a global non-splitting nature, while locally split at lifted cusps, indicating complex interactions between modular representations.