{"ddc":["510"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"quality_controlled":"1","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","text":"We prove that the $k$-th positive integer moment of partial sums of Steinhaus random multiplicative functions over the interval $(x, x+H]$ matches the corresponding Gaussian moment, as long as $H\\ll x/(\\log x)^{2k^2+2+o(1)}$ and $H$ tends to infinity with $x$. We show that properly normalized partial sums of typical multiplicative functions arising from realizations of random multiplicative functions have Gaussian limiting distribution in short moving intervals $(x, x+H]$ with $H\\ll X/(\\log X)^{W(X)}$ tending to infinity with $X$, where $x$ is uniformly chosen from $\\{1,2,\\dots, X\\}$, and $W(X)$ tends to infinity with $X$ arbitrarily slowly. This makes some initial progress on a recent question of Harper."}],"intvolume":"        18","license":"https://creativecommons.org/licenses/by/4.0/","scopus_import":"1","oa_version":"Published Version","oa":1,"page":"389-408","volume":18,"publication":"Algebra & Number Theory","status":"public","publication_identifier":{"eissn":["1944-7833"],"issn":["1937-0652"]},"publication_status":"published","date_updated":"2024-08-21T06:58:43Z","_id":"17449","title":"Partial sums of typical multiplicative functions over short moving intervals","month":"02","date_created":"2024-08-20T08:48:26Z","day":"06","article_processing_charge":"Yes (via OA deal)","file":[{"date_created":"2024-08-21T06:46:56Z","content_type":"application/pdf","checksum":"1e3467a14de754bf8d3bff03a015e1ce","date_updated":"2024-08-21T06:46:56Z","success":1,"file_id":"17455","file_size":1401725,"relation":"main_file","access_level":"open_access","file_name":"2024_AlgebraNumberTheory_Pandey.pdf","creator":"dernst"}],"author":[{"first_name":"Mayank","last_name":"Pandey","full_name":"Pandey, Mayank"},{"first_name":"Victor","full_name":"Wang, Victor","orcid":"0000-0002-0704-7026","last_name":"Wang","id":"76096395-aea4-11ed-a680-ab8ebbd3f1b9"},{"first_name":"Max Wenqiang","full_name":"Xu, Max Wenqiang","last_name":"Xu"}],"type":"journal_article","extern":"1","article_type":"original","acknowledgement":"We thank Andrew Granville and the anonymous referee for many detailed comments that led us to significantly improve the results and presentation of our work. We thank and Adam Harper for helpful discussions and useful comments and corrections on earlier versions. We also thank Yuqiu Fu, Larry Guth, Kannan Soundararajan, Katharine Woo, and Liyang Yang for helpful discussions. Finally, we thank Peter Sarnak for introducing us (the authors) to each other during the “50 Years of Number Theory and Random Matrix Theory” Conference at IAS and making the collaboration possible. \r\nOpen Access made possible by participating institutions via Subscribe to Open.","year":"2024","external_id":{"arxiv":["2207.11758"]},"file_date_updated":"2024-08-21T06:46:56Z","doi":"10.2140/ant.2024.18.389","issue":"2","citation":{"ista":"Pandey M, Wang V, Xu MW. 2024. Partial sums of typical multiplicative functions over short moving intervals. Algebra &#38; Number Theory. 18(2), 389–408.","mla":"Pandey, Mayank, et al. “Partial Sums of Typical Multiplicative Functions over Short Moving Intervals.” <i>Algebra &#38; Number Theory</i>, vol. 18, no. 2, Mathematical Sciences Publishers, 2024, pp. 389–408, doi:<a href=\"https://doi.org/10.2140/ant.2024.18.389\">10.2140/ant.2024.18.389</a>.","ama":"Pandey M, Wang V, Xu MW. Partial sums of typical multiplicative functions over short moving intervals. <i>Algebra &#38; Number Theory</i>. 2024;18(2):389-408. doi:<a href=\"https://doi.org/10.2140/ant.2024.18.389\">10.2140/ant.2024.18.389</a>","apa":"Pandey, M., Wang, V., &#38; Xu, M. W. (2024). Partial sums of typical multiplicative functions over short moving intervals. <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/ant.2024.18.389\">https://doi.org/10.2140/ant.2024.18.389</a>","short":"M. Pandey, V. Wang, M.W. Xu, Algebra &#38; Number Theory 18 (2024) 389–408.","ieee":"M. Pandey, V. Wang, and M. W. Xu, “Partial sums of typical multiplicative functions over short moving intervals,” <i>Algebra &#38; Number Theory</i>, vol. 18, no. 2. Mathematical Sciences Publishers, pp. 389–408, 2024.","chicago":"Pandey, Mayank, Victor Wang, and Max Wenqiang Xu. “Partial Sums of Typical Multiplicative Functions over Short Moving Intervals.” <i>Algebra &#38; Number Theory</i>. Mathematical Sciences Publishers, 2024. <a href=\"https://doi.org/10.2140/ant.2024.18.389\">https://doi.org/10.2140/ant.2024.18.389</a>."},"publisher":"Mathematical Sciences Publishers","date_published":"2024-02-06T00:00:00Z","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2207.11758"}]}