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This research establishes a link between the MDC-X framework and the geometric principles in Deligne’s proof related to the Ramanujan-Petersson conjecture.

June 1, 2026Open Access

Structural Integration of the Mahapatra-Dalvi-Collatz-X (MDC-X) Invariant inside -adic Etale Cohomology and ´ Hecke L-Functions

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This research establishes a link between the MDC-X framework and the geometric principles in Deligne’s proof related to the Ramanujan-Petersson conjecture.
Developed a rigorous dictionary bridging arithmetic to geometric frameworks.
Analyzed behaviors under the generalized Collatz map and derived topological invariants.
Constructed a Banach space operator to retrieve spectral poles related to integer bases.
Identified invariant ∆(3)=4 ln 99 as an eigenvalue under specific Galois representations.
Demonstrated non-modularity of the representation for dissipative multiplier a=3 signaling dissolution of the Collatz conjecture.
Characterized explicit identification of Hecke eigenvalues in relation to integer base B(a).

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Implication

This randomized trial identifies the Hecke eigenvalue and its implications in the framework of arithmetic geometry, suggesting a new relationship between number theory and topology.

Cite This Study

Dillip Kumar Mahapatra (2026) studied this question.

synapsesocial.com/papers/6a1d226d02fbce91306382e7 https://doi.org/10.5281/zenodo.20453753

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Implication

This randomized trial identifies the Hecke eigenvalue and its implications in the framework of arithmetic geometry, suggesting a new relationship between number theory and topology.

Structural Integration of the Mahapatra-Dalvi-Collatz-X (MDC-X) Invariant inside -adic Etale Cohomology and ´ Hecke L-Functions

Key Points

Discussion

Implication

Cite This Study

Structural Integration of the Mahapatra-Dalvi-Collatz-X (MDC-X) Invariant inside -adic Etale Cohomology and ´ Hecke L-Functions

Key Points

Discussion

Implication

Cite This Study

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