Interpolated Apéry-like Sequences Connect Six Sporadic Cases to Modular L-Values — E8 Intelligence Research

July 22, 2026Open Access

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Key Points

Examine the connection between interpolated Apéry-like sequences and critical L-values of modular forms.
Analyzed Apéry numbers for ζ(3) and derived recurrence relations.
Generalized findings to six sporadic sequences associated with modular forms of weights 2, 3, and 4.
Explored the relationship between modular forms and elliptic curves.
Identified critical L-values corresponding to the six sporadic sequences linked to root systems (A, D, E).
Showed that Apéry-like sequences extend Zagier’s previous work with ζ(3), linking deeper mathematical concepts.
Demonstrated that critical L-values relate to the arithmetic structure outlined in the Birch–Swinnerton-Dyer conjecture.

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Connects critical L-values of modular forms with six sporadic sequences, highlighting important mathematical implications.

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Andrew Stewart Caldin (2026) studied this question.

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