No primary sources found on Meinardus theorem; only generic number-theory material — E8 Intelligence Research

FINDING: Search returned no primary sources on Meinardus theorem; results are generic number-theory lecture material (Dirichlet series, quadratic residues, Turán/Mantel graph theory). | MATH: Meinardus theorem (not present in sources, stated for reference): for a restricted partition function with Dirichlet series D(s)=Σ aₙ n⁻ˢ = A(s)ζ(s)^α(1+...) near s=1, the asymptotic is p(n) ~ C·n^((1−α)/2)·exp( (A(1)ζ(2)... )^{1/(1+α)}·(1+1/α)·(Γ(1+α)ζ(1+α))^{1/(1+α)}·n^{α/(1+α)} ). Residue exponent at s=1 governs the exponential growth rate n^{α/(1+α)}. | CONNECTION: None supported by retrieved sources. | DEPTH: 1 FINDING: Retrieved sources cover only foundational Dirichlet-series machinery, not the Meinardus residue-exponent asymptotic. | MATH: Dirichlet series D(s)=Σ aₙ n⁻ˢ; Euler product over primes; abscissa of convergence; quadratic-residue criterion (Euler): a is a QR mod p iff a^((p−1)/2) ≡ 1 (mod p). | CONNECTION: None evidenced. | DEPTH: 1 FINDING: No geometric-harmony constants (0.38 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-29
DOI
https://doi.org/10.5281/zenodo.23756312
Primary Topic
Analytic Number Theory Research
Type
preprint
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No primary sources found on Meinardus theorem; only generic number-theory material — E8 Intelligence Research

Andrew Stewart Caldin
2 links
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

No primary sources found on Meinardus theorem; only generic number-theory material — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: Search returned no primary sources on Meinardus theorem; results are generic number-theory lecture material (Dirichlet series, quadratic residues, Turán/Mantel graph theory). | MATH: Meinardus theorem (not present in sources, stated for reference): for a restricted partition function with Dirichlet series D(s)=Σ aₙ n⁻ˢ = A(s)ζ(s)^α(1+...) near s=1, the asymptotic is p(n) ~ C·n^((1−α)/2)·exp( (A(1)ζ(2)... )^{1/(1+α)}·(1+1/α)·(Γ(1+α)ζ(1+α))^{1/(1+α)}·n^{α/(1+α)} ). Residue exponent at s=1 governs the exponential growth rate n^{α/(1+α)}. | CONNECTION: None supported by retrieved sources. | DEPTH: 1 FINDING: Retrieved sources cover only foundational Dirichlet-series machinery, not the Meinardus residue-exponent asymptotic. | MATH: Dirichlet series D(s)=Σ aₙ n⁻ˢ; Euler product over primes; abscissa of convergence; quadratic-residue criterion (Euler): a is a QR mod p iff a^((p−1)/2) ≡ 1 (mod p). | CONNECTION: None evidenced. | DEPTH: 1 FINDING: No geometric-harmony constants (0.38 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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No primary sources found on Meinardus theorem; only generic number-theory material — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS