Sums of divisor functions and von Mangoldt convolutions in 𝔽q[T] leading to symplectic distributions Kuperberg, Vivian Zieve Lalín, Matilde In [J. P. Keating, B. Rodgers, E. Roditty-Gershon and Z. Rudnick, Sums of divisor functions in 𝔽𝑞⁢[𝑡] and matrix integrals, Math. Z. 288 2018, 1–2, 167–198], the authors established relationships of the mean-square of sums of the divisor function 𝑑𝑘⁢(𝑓) over short intervals and over arithmetic progressions for the function field 𝔽𝑞⁢[𝑇] to certain integrals over the ensemble of unitary matrices. We consider similar problems leading to distributions over the ensemble of symplectic matrices. We also consider analogous questions involving convolutions of the von Mangoldt function. De Gruyter 2022 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22194 Kuperberg VZ, Lalín M. Sums of divisor functions and von Mangoldt convolutions in 𝔽q[T] leading to symplectic distributions. <i>Forum Mathematicum</i>. 2022;34(3):711-747. doi:<a href="https://doi.org/10.1515/forum-2021-0171">10.1515/forum-2021-0171</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1515/forum-2021-0171 info:eu-repo/semantics/altIdentifier/issn/0933-7741 info:eu-repo/semantics/altIdentifier/e-issn/1435-5337 info:eu-repo/semantics/altIdentifier/arxiv/2107.01437 info:eu-repo/semantics/openAccess