Toric extensions of Pólya's theorem
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914147446292480 |
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| author | Baldi, Lorenzo Sinn, Rainer Telek, Máté L. Weigert, Julian |
| author_facet | Baldi, Lorenzo Sinn, Rainer Telek, Máté L. Weigert, Julian |
| contents | The classical version of Pólya's theorem provides a simple method for certifying that a homogeneous polynomial of degree d is strictly copositive, that is, it takes only positive values on the nonnegative real orthant. However, this method might fail to detect copositivity of polynomials that are missing certain degree d monomials. In this paper, we present extensions and converses to Pólya's theorem for sparse polynomials, using techniques from positive toric geometry. Furthermore, we explore how this method can be used to study the convergence of Feynman integrals in particle physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07342 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toric extensions of Pólya's theorem Baldi, Lorenzo Sinn, Rainer Telek, Máté L. Weigert, Julian Algebraic Geometry 14M25, 14P99 The classical version of Pólya's theorem provides a simple method for certifying that a homogeneous polynomial of degree d is strictly copositive, that is, it takes only positive values on the nonnegative real orthant. However, this method might fail to detect copositivity of polynomials that are missing certain degree d monomials. In this paper, we present extensions and converses to Pólya's theorem for sparse polynomials, using techniques from positive toric geometry. Furthermore, we explore how this method can be used to study the convergence of Feynman integrals in particle physics. |
| title | Toric extensions of Pólya's theorem |
| topic | Algebraic Geometry 14M25, 14P99 |
| url | https://arxiv.org/abs/2511.07342 |