What question did this study set out to answer?

The research aims to explore the behavior of symmetric-cube hypergeometric coefficients at mixed CM points and their implications in supercongruences.

April 7, 2026Open Access

Split-prime supercongruences at a mixed CM point: order drop, Eisenstein dichotomy, and reduction to a unit-root congruence

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The research aims to explore the behavior of symmetric-cube hypergeometric coefficients at mixed CM points and their implications in supercongruences.
Analyzed symmetric-cube hypergeometric coefficients at mixed CM points.
Examined the effects of split versus inert primes on Eisenstein pieces.
Conducted computational verification of congruences for split primes up to 31.
Established an arithmetic dichotomy based on Eisenstein decomposition.
Identified cases where natural bivariate congruences fail.
Reduced the full split-prime supercongruence to six explicit scalar congruences.

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Implication

Uncovers arithmetic characteristics of supercongruences at mixed CM points, suggesting deeper connections in number theory.

Cite This Study

Alex Shvets (2026) studied this question.

synapsesocial.com/papers/69d49fe5b33cc4c35a228658 https://doi.org/10.5281/zenodo.19425332

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Split-prime supercongruences at a mixed CM point: order drop, Eisenstein dichotomy, and reduction to a unit-root congruence

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Implication

Cite This Study

Split-prime supercongruences at a mixed CM point: order drop, Eisenstein dichotomy, and reduction to a unit-root congruence

Key Points

Discussion

Implication

Cite This Study

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