Zagier's Interpolation Links Apéry Numbers to Modular L-Functions — E8 Intelligence Research

July 20, 2026Open Access

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Key Points

The study seeks to establish connections between Apéry numbers and modular L-functions through Zagier's interpolation.
Derivation of Apéry numbers using combinatorial principles and generating functions.
Establishment of the modular form of weight 4 corresponding to the critical L-value.
Analysis of sporadic sequences defined by recurrence relations with specific parameters.
Zagier's interpolation links Apéry numbers to critical L-values of modular forms, enhancing their understanding in number theory.
Demonstration that the interpolated generating function aligns with weight-4 modular forms at the critical value.
Connection established between weight-4 modular forms and the root lattice E8 through mathematical structures.

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Links Apéry numbers and modular forms in mathematical exploration, suggesting deeper connections in number theory.

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Andrew Stewart Caldin (2026) studied this question.

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