{"id":22,"date":"2012-09-05T11:22:33","date_gmt":"2012-09-05T15:22:33","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/template\/?page_id=22"},"modified":"2026-03-19T08:14:53","modified_gmt":"2026-03-19T12:14:53","slug":"research","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/alladik\/research\/","title":{"rendered":"Recent Papers"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">Recent Papers<\/h1>\n\n\n\n<p>(Updated 10.02.2024)<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>(with Yazan Alamoudi) &#8220;Some q-hypergeometric identities associated with the partition theorems of Lebesgue, Schur, and Capparelli&#8221; (2025 preprint)\n<\/li><li><a href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">\u201c (with Jason Johnson) Duality between prime factors andPrime Number theorem for Arithmetic Progressions \u2013 II (2024 Preprint)\u201d<\/a>  See also &#8211; <a href=\"https:\/\/arxiv.org\/abs\/2410.18259\">ArXiV 2410.18259<\/a> [math.NT]<\/li>\n<li>\n<div class=\"elementToProof\"><a href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\"><span class=\"ContentPasted0\"> \u201cSchmidt-type theorems via weighted <\/span><span class=\"ContentPasted0\">partition identities\u201d, Ramanujan J., Askey Memorial <\/span><span class=\"ContentPasted0\">Issues,<b>61<\/b> (2023, 701-714).<\/span><\/a><\/div>\n<\/li>\n<li>\n<div><a href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">(with Ankush Goswami) \u201cParity results concerning the generalized <\/a><\/div>\n<div><a href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">divisor function involving small prime factors of integers\u201d- Dec 2021 preprint<\/a><\/div>\n<div><a href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">(To the memory of Prof. M. V. Subbarao on his Centenary)<\/a><\/div>\n<\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">\u201cEuler\u2019s partition theorem and refinements without appeal to infinite products\u201d <em>Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra \u2013 in honor of Peter Paule for his 60th Birthday<\/em> (V. Pillwein and C. Schneider, Eds.), Texts and Monographs in Symbolic Computation, Springer, Switzerland (2020), 9-23. <\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">\u201cMy association and collaboration with George Andrews \u2013 still going strong at 80\u201d <em>George E. Andrews, 80 years of Combinatory Analysis<\/em> (K. Alladi, B. C. Berndt, P. Paule, J. A. Sellers, A. J. Yee \u2013 Eds.), Trends in Math. Series, Birkhauser, Switzerland (2021), 9-31<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">\u201cRamanujan\u2019s legacy \u2013 the work of the SASTRA Prize winners\u201d Philosophical Transactions of the Royal Society, Vol. 378 (2020), 1-19. (Special Issue in celebration of the centenary of Ramanujan\u2019s election as FRS)<\/a><\/li>\n<li><a style=\"font-size: inherit\" href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">(With Todd Molnar) On the local distribution of the number of small prime factors \u2013 a variation of the classical theme, Ramanujan J., Vol. 51 (2020), pp 117-151.<\/a><\/li>\n<li><a href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">Partitions with non-repeating odd parts and combinatorial identities, Annals of Combinatorics (Annals of Combinatorics, <b>20<\/b> (2016), 1-20.)<\/a><\/li>\n<li><a style=\"font-size: inherit\" href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">(with George E. Andrews), The dual of Gollnitz\u2019 (Big) partition theorem, The Ramanujan Journal \u2013 Basil Gordon Memorial Issues, 36 (2015), 171-201.<\/a><\/li>\n<li><a style=\"font-size: inherit\" href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">Partial theta identities of Ramanujan, Andrews, and Rogers-Fine involving the squares, in The Legacy of Srinivasa Ramanujan, Proc. Ramanujan 125 Conf., New Delhi 2012, RMS-Lecture Notes Series 20 (2013), 29-53<\/a><\/li>\n<li><a style=\"font-size: inherit\" href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">A multi-dimensional extension of Sylvester\u2019s identity, International Journal of Number Theory <b>13<\/b> (2017) 2487-2504<\/a><\/li>\n<li>(With Colin Defant) <a href=\"https:\/\/people.clas.ufl.edu\/alladik\/content-removed\/\">Revisiting the Riemann zeta function at the even positive integers<\/a>, International Journal of Number Theory, <b>14<\/b> (2018), 1849-1856.<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Solo papers of my PhD student based on my work<\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>Yazan Alamoudi: &#8220;A bijective proof of Andrews&#8217; refinement of the Alladi-Schur theorem&#8221; (2024 preprint) &#8211; see arXiv: 2410.15630 [math.NT]\n<\/li><li>Sroyon Sengupta: &#8220;Algebraic analogues of the results of Alladi-Johnson using the Chebotarev density theorem&#8221; (2024 preprint) &#8211; see arXiv: 2410.22226 [math. NT]\n<\/li><\/ul>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":283,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-22","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/pages\/22","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/users\/283"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/comments?post=22"}],"version-history":[{"count":11,"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/pages\/22\/revisions"}],"predecessor-version":[{"id":743,"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/pages\/22\/revisions\/743"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/alladik\/wp-json\/wp\/v2\/media?parent=22"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}