Order drop, Hecke descent, and an unconditional mod p⁴ supercongruence for Sym³ hypergeometric coefficients

Key Points

• The research aims to establish a supercongruence for specific coefficients of the symmetric cube of the hypergeometric function.
• Combined modular identification on X_0(3)
• Utilized Eisenstein-type congruence for Hauptmodul coefficients
• Applied Fricke–Hecke descent argument for defect vanishing
• Proved supercongruence modulo p to the fourth
• Demonstrated uniform vanishing of all defects in the coefficients
• Provided insights into the mathematical relationships among hypergeometric coefficients

Abstract