{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:30:08Z","timestamp":1760059808119,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,12]],"date-time":"2025-07-12T00:00:00Z","timestamp":1752278400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union-Next Generation EU through the National Recovery and Resilience Plan of the Republic of Bulgaria","award":["DUECOS BG-RRP-2.004-0001-C01"],"award-info":[{"award-number":["DUECOS BG-RRP-2.004-0001-C01"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Let \u03b1,\u03b2\u2208R with \u03b1\u22600, and let \u03b3\u2208(0,5\/6). Define the set M1 to consist of primes p such that p+2 is almost prime, and let M2 be the set of primes of the form p=a2+b2+1. We study the distribution of \u03b1p\u03b3\u00a0+\u00a0\u03b2 modulo one, as p ranges over the sets M1 and M2, respectively.<\/jats:p>","DOI":"10.3390\/axioms14070532","type":"journal-article","created":{"date-parts":[[2025,7,14]],"date-time":"2025-07-14T10:55:41Z","timestamp":1752490541000},"page":"532","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Distribution Modulo One of \u03b1p\u03b3 + \u03b2 for Special Classes of Primes"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7377-9121","authenticated-orcid":false,"given":"Atanaska","family":"Georgieva","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0121-3206","authenticated-orcid":false,"given":"Tatiana L.","family":"Todorova","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Informatics, Sofia University \u201dSt. Kliment Ohridski\u201d, 1504 Sofia, Bulgaria"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/BF02401833","article-title":"Some problems of Diophantine approximation I. 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(In Russian)."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/7\/532\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:09:10Z","timestamp":1760033350000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/7\/532"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,7,12]]},"references-count":26,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["axioms14070532"],"URL":"https:\/\/doi.org\/10.3390\/axioms14070532","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,7,12]]}}}