Sums of divisor functions and von Mangoldt convolutions in 𝔽q[T] leading to symplectic distributions

article Sums of divisor functions and von Mangoldt convolutions in 𝔽q[T] leading to symplectic distributions published yes Vivian Zieve Kuperberg author c3bac823-112d-11f0-a3f5-c264f852e697 Matilde Lalín author 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 Gruyter2022 eng Forum Mathematicum 0933-7741 1435-5337 2107.0143710.1515/forum-2021-0171 343711-747 yes Kuperberg, V. Z., & Lalín, M. (2022). Sums of divisor functions and von Mangoldt convolutions in 𝔽q[T] leading to symplectic distributions. Forum Mathematicum. De Gruyter. <a href="https://doi.org/10.1515/forum-2021-0171">https://doi.org/10.1515/forum-2021-0171</a> V. Z. Kuperberg and M. Lalín, “Sums of divisor functions and von Mangoldt convolutions in 𝔽q[T] leading to symplectic distributions,” Forum Mathematicum, vol. 34, no. 3. De Gruyter, pp. 711–747, 2022. Kuperberg VZ, Lalín M. 2022. Sums of divisor functions and von Mangoldt convolutions in 𝔽q[T] leading to symplectic distributions. Forum Mathematicum. 34(3), 711–747. Kuperberg, Vivian Zieve, and Matilde Lalín. “Sums of Divisor Functions and von Mangoldt Convolutions in 𝔽q[T] Leading to Symplectic Distributions.” Forum Mathematicum, vol. 34, no. 3, De Gruyter, 2022, pp. 711–47, doi:<a href="https://doi.org/10.1515/forum-2021-0171">10.1515/forum-2021-0171</a>. Kuperberg, Vivian Zieve, and Matilde Lalín. “Sums of Divisor Functions and von Mangoldt Convolutions in 𝔽q[T] Leading to Symplectic Distributions.” Forum Mathematicum. De Gruyter, 2022. <a href="https://doi.org/10.1515/forum-2021-0171">https://doi.org/10.1515/forum-2021-0171</a>. Kuperberg VZ, Lalín M. Sums of divisor functions and von Mangoldt convolutions in 𝔽q[T] leading to symplectic distributions. Forum Mathematicum. 2022;34(3):711-747. doi:<a href="https://doi.org/10.1515/forum-2021-0171">10.1515/forum-2021-0171</a> V.Z. Kuperberg, M. Lalín, Forum Mathematicum 34 (2022) 711–747. 221942026-06-29T12:57:26Z2026-07-14T11:02:45Z