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Additionally, we explore the implications of these findings, highlighting their relevance to Salem\u2019s equivalence and potential connections with the Riemann hypothesis.<\/jats:p>","DOI":"10.3390\/axioms14110814","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T19:30:27Z","timestamp":1762198227000},"page":"814","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Some New Applications of the Mellin Transform Involving the Lambert Transforms and Implications for the Riemann Hypothesis"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9277-8092","authenticated-orcid":false,"given":"Hari M.","family":"Srivastava","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea"},{"name":"Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan City 320314, Taiwan"},{"name":"Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, Baku AZ1007, Azerbaijan"},{"name":"Section of Mathematics, International Telematic University Uninettuno, 39 Corso Vittorio Emanuele II, I-00186 Rome, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6569-8540","authenticated-orcid":false,"given":"Jeetendrasingh","family":"Maan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Scientific Computing, National Institute of Technology, Hamirpur 177005, India"}]},{"given":"Emilio R.","family":"Negr\u00edn","sequence":"additional","affiliation":[{"name":"Departamento de An\u00e1lisis Matem\u00e1tico, Facultad de Ciencias, Universidad de La Laguna (ULL), Campus de Anchieta, ES-38271 La Laguna, Tenerife, Spain"},{"name":"Instituto de Matem\u00e1ticas y Aplicaciones (IMAULL), Universidad de La Laguna (ULL), ULL Campus de Anchieta, ES-38271 La Laguna, Tenerife, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,31]]},"reference":[{"key":"ref_1","unstructured":"Zayed, A.I. 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