[{"date_updated":"2026-07-14T11:20:10Z","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"01","article_type":"original","OA_place":"repository","author":[{"id":"c3bac823-112d-11f0-a3f5-c264f852e697","first_name":"Vivian Zieve","last_name":"Kuperberg","full_name":"Kuperberg, Vivian Zieve"},{"full_name":"Lalín, Matilde","first_name":"Matilde","last_name":"Lalín"}],"title":"Arithmetic constants for symplectic variances of the divisor function","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2410.17939","open_access":"1"}],"oa":1,"external_id":{"arxiv":["2410.17939"]},"arxiv":1,"OA_type":"green","publication_identifier":{"issn":["0025-5793","2041-7942"]},"date_published":"2025-05-01T00:00:00Z","extern":"1","publication":"Mathematika","_id":"22199","mathsc":["11N60","05A15","11M50","11N56"],"date_created":"2026-06-29T12:59:16Z","oa_version":"Preprint","article_number":"e70029","volume":71,"language":[{"iso":"eng"}],"year":"2025","quality_controlled":"1","issue":"3","month":"05","article_processing_charge":"No","abstract":[{"text":"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.","lang":"eng"}],"citation":{"ista":"Kuperberg VZ, Lalín M. 2025. Arithmetic constants for symplectic variances of the divisor function. Mathematika. 71(3), e70029.","ieee":"V. Z. Kuperberg and M. Lalín, “Arithmetic constants for symplectic variances of the divisor function,” <i>Mathematika</i>, vol. 71, no. 3. Wiley, 2025.","chicago":"Kuperberg, Vivian Zieve, and Matilde Lalín. “Arithmetic Constants for Symplectic Variances of the Divisor Function.” <i>Mathematika</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/mtk.70029\">https://doi.org/10.1112/mtk.70029</a>.","short":"V.Z. Kuperberg, M. Lalín, Mathematika 71 (2025).","ama":"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>","apa":"Kuperberg, V. Z., &#38; Lalín, M. (2025). Arithmetic constants for symplectic variances of the divisor function. <i>Mathematika</i>. Wiley. <a href=\"https://doi.org/10.1112/mtk.70029\">https://doi.org/10.1112/mtk.70029</a>","mla":"Kuperberg, Vivian Zieve, and Matilde Lalín. “Arithmetic Constants for Symplectic Variances of the Divisor Function.” <i>Mathematika</i>, vol. 71, no. 3, e70029, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/mtk.70029\">10.1112/mtk.70029</a>."},"doi":"10.1112/mtk.70029","scopus_import":"1","intvolume":"        71","publisher":"Wiley","type":"journal_article","publication_status":"published"}]