Arithmetic constants for symplectic variances of the divisor function Kuperberg, Vivian Zieve Lalín, Matilde Kuperberg and Lalín stated some conjectures on the variance of certain sums of the divisor function dk(n) over number fields, which were inspired by analogous results over function fields proven by the authors. These problems are related to certain symplectic matrix integrals. While the function field results can be directly related to the random matrix integrals, the connection between the random matrix integrals and the number field results is less direct and involves arithmetic factors. The goal of this article is to give heuristic arguments for the formulas of these arithmetic factors. Wiley 2025 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22199 Kuperberg VZ, Lalín M. Arithmetic constants for symplectic variances of the divisor function. <i>Mathematika</i>. 2025;71(3). doi:<a href="https://doi.org/10.1112/mtk.70029">10.1112/mtk.70029</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1112/mtk.70029 info:eu-repo/semantics/altIdentifier/issn/0025-5793 info:eu-repo/semantics/altIdentifier/issn/2041-7942 info:eu-repo/semantics/altIdentifier/arxiv/2410.17939 info:eu-repo/semantics/openAccess