Algebraic Theta Functions and Eisenstein-Kronecker Numbers: A Research Overview — E8 Intelligence Research

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Eisenstein-Kronecker numbers, evaluated at special values, act as periods of elliptic curves related to L-values of Hecke characters, and possess distinct p-adic and algebraic properties. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22702095

September 11, 2026Open Access

Algebraic Theta Functions and Eisenstein-Kronecker Numbers: A Research Overview — E8 Intelligence Research

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Key Points

To synthesize the algebraic and p-adic properties of Eisenstein-Kronecker numbers and analyze their connections to algebraic theta functions, elliptic curve periods, and special L-values.
Evaluated Eisenstein-Kronecker summation series at special values using Kronecker limit formulas.
Applied Mumford theory of algebraic theta functions to construct algebraic models of abelian varieties and study p-adic properties.
Identified Eisenstein-Kronecker numbers as period integrals of elliptic curves directly corresponding to L-values of Hecke characters.
Formulated algebraic relationships linking Dedekind zeta evaluations at s=1 to the fundamental periods of complex multiplication elliptic curves.

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Implication

Theoretical review uncovers algebraic and p-adic structures of Eisenstein-Kronecker numbers in abelian varieties, highlighting links between theta functions and special L-values.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6aa7b3660926e14a848b246f https://doi.org/10.5281/zenodo.22702095

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Algebraic Theta Functions and Eisenstein-Kronecker Numbers: A Research Overview — E8 Intelligence Research

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Algebraic Theta Functions and Eisenstein-Kronecker Numbers: A Research Overview — E8 Intelligence Research

Key Points

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