{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:00:01Z","timestamp":1776844801963,"version":"3.51.2"},"reference-count":22,"publisher":"American Mathematical Society (AMS)","issue":"298","license":[{"start":{"date-parts":[[2016,10,7]],"date-time":"2016-10-07T00:00:00Z","timestamp":1475798400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    Let\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"psi Subscript double-struck upper K\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>\n                              \u03c8\n                              \n                            <\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"double-struck\">K<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\psi _{\\mathbb {K}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    be the Chebyshev function of a number field\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper K\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi mathvariant=\"double-struck\">K<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {K}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Under the Generalized Riemann Hypothesis we prove an explicit upper bound for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"StartAbsoluteValue psi Subscript double-struck upper K Baseline left-parenthesis x right-parenthesis minus x EndAbsoluteValue\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo stretchy=\"false\">|<\/mml:mo>\n                            <\/mml:mrow>\n                            <mml:msub>\n                              <mml:mi>\n                                \u03c8\n                                \n                              <\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mi mathvariant=\"double-struck\">K<\/mml:mi>\n                                <\/mml:mrow>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                            <mml:mo>\n                              \u2212\n                              \n                            <\/mml:mo>\n                            <mml:mi>x<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo stretchy=\"false\">|<\/mml:mo>\n                            <\/mml:mrow>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">|\\psi _{\\mathbb {K}}(x)-x|<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in terms of the degree and the discriminant of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper K\">\n                        <mml:semantics>\n                          <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                            <mml:mi mathvariant=\"double-struck\">K<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {K}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . The new bound improves significantly on previous known results.\n                  <\/p>","DOI":"10.1090\/mcom3031","type":"journal-article","created":{"date-parts":[[2015,2,4]],"date-time":"2015-02-04T10:52:49Z","timestamp":1423047169000},"page":"889-906","source":"Crossref","is-referenced-by-count":12,"title":["Explicit versions of the prime ideal theorem for Dedekind zeta functions under GRH"],"prefix":"10.1090","volume":"85","author":[{"given":"Lo\u00efc","family":"Greni\u00e9","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giuseppe","family":"Molteni","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,10,7]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"263","DOI":"10.4064\/aa-40-3-263-271","article-title":"On a result of Littlewood concerning prime numbers","volume":"40","author":"Goldston, D. 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