Second-Order q-Dependence in the Clock-Model Spectral Baseline: q = 3 as the Unique Exception

Companion to Paper #7. Proves α_q(1) = 0 for all q ≠ 3 (exact, by Fourier orthogonality on ℤ/qℤ), α₃ = 3/4. Second-order L-function connection: K₃⁽²⁾ = c·(3/4)·L(2,χ₃)·(βJ)². Universality holds at second order for all q ≠ 3.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-04
DOI
https://doi.org/10.5281/zenodo.23944634
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Second-Order q-Dependence in the Clock-Model Spectral Baseline: q = 3 as the Unique Exception

Adrian *Tusk Sutton
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Second-Order q-Dependence in the Clock-Model Spectral Baseline: q = 3 as the Unique Exception

Adrian *Tusk Sutton
preprint en

Abstract

Companion to Paper #7. Proves α_q(1) = 0 for all q ≠ 3 (exact, by Fourier orthogonality on ℤ/qℤ), α₃ = 3/4. Second-order L-function connection: K₃⁽²⁾ = c·(3/4)·L(2,χ₃)·(βJ)². Universality holds at second order for all q ≠ 3.

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Second-Order q-Dependence in the Clock-Model Spectral Baseline: q = 3 as the Unique Exception — Adrian *Tusk Sutton · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS