[{"intvolume":"       131","mathsc":["11N69","11N05","14G05"],"publication_status":"published","oa":1,"extern":"1","doi":"10.1112/plms.70068","language":[{"iso":"eng"}],"author":[{"full_name":"Bloom, Thomas F.","last_name":"Bloom","first_name":"Thomas F."},{"id":"c3bac823-112d-11f0-a3f5-c264f852e697","full_name":"Kuperberg, Vivian Zieve","last_name":"Kuperberg","first_name":"Vivian Zieve"}],"article_type":"original","date_created":"2026-06-29T13:00:46Z","year":"2025","publication":"Proceedings of the London Mathematical Society","OA_place":"repository","day":"01","_id":"22203","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","issue":"1","month":"07","quality_controlled":"1","date_updated":"2026-07-14T11:45:18Z","external_id":{"arxiv":["2312.09021"]},"arxiv":1,"article_processing_charge":"No","date_published":"2025-07-01T00:00:00Z","title":"Odd moments and adding fractions","volume":131,"status":"public","type":"journal_article","publication_identifier":{"issn":["0024-6115"],"eissn":["1460-244X"]},"OA_type":"green","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2312.09021","open_access":"1"}],"publisher":"Wiley","abstract":[{"lang":"eng","text":"We prove near-optimal upper bounds for the oddmoments of the distribution of coprime residues inshort intervals, confirming a conjecture of Montgomeryand Vaughan. As an application, we prove near-optimalupper bounds for the average of the refined singularseries in the Hardy–Littlewood conjectures concerningthe number of prime 𝑘-tuples for 𝑘 odd. The mainnew ingredient is a near-optimal upper bound for thenumber of solutions to ∑1 ⩽𝑖 ⩽𝑘𝑎 𝑖𝑞𝑖∈ ℤ when 𝑘 is odd,with gcd(𝑎𝑖 , 𝑞𝑖 ) = 1 and restrictions on the size of thenumerators and denominators, which is of indepen-dent interest."}],"scopus_import":"1","citation":{"ieee":"T. F. Bloom and V. Z. Kuperberg, “Odd moments and adding fractions,” <i>Proceedings of the London Mathematical Society</i>, vol. 131, no. 1. Wiley, 2025.","ama":"Bloom TF, Kuperberg VZ. Odd moments and adding fractions. <i>Proceedings of the London Mathematical Society</i>. 2025;131(1). doi:<a href=\"https://doi.org/10.1112/plms.70068\">10.1112/plms.70068</a>","chicago":"Bloom, Thomas F., and Vivian Zieve Kuperberg. “Odd Moments and Adding Fractions.” <i>Proceedings of the London Mathematical Society</i>. Wiley, 2025. <a href=\"https://doi.org/10.1112/plms.70068\">https://doi.org/10.1112/plms.70068</a>.","apa":"Bloom, T. F., &#38; Kuperberg, V. Z. (2025). Odd moments and adding fractions. <i>Proceedings of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/plms.70068\">https://doi.org/10.1112/plms.70068</a>","short":"T.F. Bloom, V.Z. Kuperberg, Proceedings of the London Mathematical Society 131 (2025).","ista":"Bloom TF, Kuperberg VZ. 2025. Odd moments and adding fractions. Proceedings of the London Mathematical Society. 131(1), e70068.","mla":"Bloom, Thomas F., and Vivian Zieve Kuperberg. “Odd Moments and Adding Fractions.” <i>Proceedings of the London Mathematical Society</i>, vol. 131, no. 1, e70068, Wiley, 2025, doi:<a href=\"https://doi.org/10.1112/plms.70068\">10.1112/plms.70068</a>."},"article_number":"e70068","oa_version":"Preprint"}]