A note on "Higher order linear differential equations for unitary matrix integrals: applications and generalisations"
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909995478548480 |
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| author | Forrester, Peter J. Wei, Fei |
| author_facet | Forrester, Peter J. Wei, Fei |
| contents | In this note, we briefly introduce the background and motivation of the collaborative work [arXiv:2508.20797], and provide an outline of the main results. The latter relates to matrix and higher order scalar differential equations satisfied by certain Hankel and Toeplitz determinants involving I-Bessel functions, or equivalently certain unitary matrix integrals, and moreover puts this property in a broader context. We also investigate large gaps between zeros of the derivatives of the Hardy $\mathsf{Z}$-function, assuming the validity of a certain joint moments conjecture in random matrix theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13488 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on "Higher order linear differential equations for unitary matrix integrals: applications and generalisations" Forrester, Peter J. Wei, Fei Mathematical Physics In this note, we briefly introduce the background and motivation of the collaborative work [arXiv:2508.20797], and provide an outline of the main results. The latter relates to matrix and higher order scalar differential equations satisfied by certain Hankel and Toeplitz determinants involving I-Bessel functions, or equivalently certain unitary matrix integrals, and moreover puts this property in a broader context. We also investigate large gaps between zeros of the derivatives of the Hardy $\mathsf{Z}$-function, assuming the validity of a certain joint moments conjecture in random matrix theory. |
| title | A note on "Higher order linear differential equations for unitary matrix integrals: applications and generalisations" |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2601.13488 |