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The research aims to analyze supercongruences at mixed CM points, focusing on order drops and modular relationships.

April 10, 2026Open Access

Split-prime supercongruences at a mixed CM point: order drop, Eisenstein dichotomy, transport cancellation, and crystalline reduction

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The research aims to analyze supercongruences at mixed CM points, focusing on order drops and modular relationships.
Investigated symmetric-cube hypergeometric coefficients at the mixed CM point (1/6, 1/3; 1)
Conducted 144 rational-arithmetic tests for various split primes
Examined transport cancellation linked to Cartier layers and Fricke-trace directions
Found that Eisenstein components share factors at split primes but not at inert primes.
Demonstrated failure of a natural bivariate congruence on the full Eisenstein module, although it holds on a specific diagonal.
Identified a staircase structure in the cancellation that relates p-adic valuations to their Fricke-trace combination.

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Explores supercongruences related to symmetric-cube coefficients, indicating key arithmetic behaviors at mixed CM points.

Alex Shvets (2026) studied this question.

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