{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T00:51:20Z","timestamp":1773795080709,"version":"3.50.1"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","license":[{"start":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T00:00:00Z","timestamp":1676419200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100004756","name":"Emil Aaltosen S\ufffd\ufffdti\ufffd","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004756","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008019","name":"\ufffdbo Akademi","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100008019","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We prove an explicit error term for the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"psi left-parenthesis x comma chi right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>\n                              \u03c8\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mi>\n                              \u03c7\n                              \n                            <\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\psi (x,\\chi )<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    function assuming the Generalized Riemann Hypothesis. Using this estimate, we prove a conditional explicit bound for the number of primes in arithmetic progressions.\n                  <\/p>","DOI":"10.1090\/mcom\/3691","type":"journal-article","created":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T09:43:10Z","timestamp":1630489390000},"source":"Crossref","is-referenced-by-count":1,"title":["Explicit bound for the number of primes in arithmetic progressions assuming the Generalized Riemann Hypothesis"],"prefix":"10.1090","author":[{"given":"Anne-Maria","family":"Ernvall-Hyt\u00f6nen","sequence":"first","affiliation":[]},{"given":"Neea","family":"Paloj\u00e4rvi","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2022,2,15]]},"reference":[{"issue":"329","key":"1","doi-asserted-by":"publisher","first-page":"1455","DOI":"10.1090\/mcom\/3599","article-title":"Counting zeros of Dirichlet \ud835\udc3f-functions","volume":"90","author":"Bennett, Michael A.","year":"2021","journal-title":"Math. 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Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"key":"6","series-title":"Graduate Texts in Mathematics","isbn-type":"print","volume-title":"Multiplicative number theory","volume":"74","author":"Davenport, Harold","year":"2000","ISBN":"https:\/\/id.crossref.org\/isbn\/0387950974","edition":"3"},{"issue":"2","key":"7","doi-asserted-by":"publisher","first-page":"Art. 19.2.2, 10","DOI":"10.1007\/s00365-018-9429-3","article-title":"Euler\u2019s divergent series in arithmetic progressions","volume":"22","author":"Ernvall-Hyt\u00f6nen, Anne-Maria","year":"2019","journal-title":"J. Integer Seq."},{"issue":"160","key":"8","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1090\/S0025-5718-1982-0669666-2","article-title":"Table errata: Table of integrals, series, and products [corrected and enlarged edition, Academic Press, New York, 1980; MR 81g:33001] by I. S. Gradshteyn [I. S. Gradshte\u012dn] and I. M. Ryzhik","volume":"39","author":"van Haeringen, H.","year":"1982","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"295","key":"9","doi-asserted-by":"publisher","first-page":"2391","DOI":"10.1090\/S0025-5718-2015-02925-1","article-title":"Conditional bounds for the least quadratic non-residue and related problems","volume":"84","author":"Lamzouri, Youness","year":"2015","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"10","unstructured":"C.-J. de la Vall\u00e9e Poussin, Recherches analytiques la th\u00e9orie des nombres premiers, Ann. Soc. Sci. Bruxelles 20 (1896), 183\u2013256."},{"key":"11","first-page":"64","article-title":"Approximate formulas for some functions of prime numbers","volume":"6","author":"Rosser, J. Barkley","year":"1962","journal-title":"Illinois J. 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