{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T14:47:57Z","timestamp":1764859677086,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,14]],"date-time":"2024-08-14T00:00:00Z","timestamp":1723593600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>By the Bagchi theorem, the Riemann hypothesis (all non-trivial zeros lie on the critical line) is equivalent to the self-approximation of the function \u03b6(s) by shifts \u03b6(s+i\u03c4). In this paper, it is determined that the Riemann hypothesis is equivalent to the positivity of density of the set of the above shifts approximating \u03b6(s) with all but at most countably many accuracies \u03b5&gt;0. Also, the analogue of an equivalent in terms of positive density in short intervals is discussed.<\/jats:p>","DOI":"10.3390\/computation12080164","type":"journal-article","created":{"date-parts":[[2024,8,14]],"date-time":"2024-08-14T03:46:36Z","timestamp":1723607196000},"page":"164","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Remarks on the Connection of the Riemann Hypothesis to Self-Approximation"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7671-0282","authenticated-orcid":false,"given":"Antanas","family":"Laurin\u010dikas","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,14]]},"reference":[{"key":"ref_1","unstructured":"Titchmarsh, E.C. (1980). 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