Positivity of Jacobi theta tails with finite denominators

We prove Zhou’s positivity conjecture for Jacobi theta tails with finite denominators. The proof combines an exact coefficient decomposition, bounds for Gaussian polynomials, a combinatorial injection, and exact finite computations.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-02
DOI
https://doi.org/10.5281/zenodo.23888345
Primary Topic
Advanced Mathematical Identities
Type
preprint
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preprint

Positivity of Jacobi theta tails with finite denominators

Haoyuan Wu
1 links
Zenodo (CERN European Organization for Nuclear Research)
Advanced Mathematical Identities
preprint

Positivity of Jacobi theta tails with finite denominators

Haoyuan Wu
preprint en

Abstract

We prove Zhou’s positivity conjecture for Jacobi theta tails with finite denominators. The proof combines an exact coefficient decomposition, bounds for Gaussian polynomials, a combinatorial injection, and exact finite computations.

Zenodo (CERN European Organization for Nuclear Research)
University of Science and Technology Liaoning (CN)
Advanced Mathematical Identities
DOIOpen Access PDFOpenAlex
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Positivity of Jacobi theta tails with finite denominators — Haoyuan Wu · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS