{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T20:49:25Z","timestamp":1776804565857,"version":"3.51.2"},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"315","license":[{"start":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T00:00:00Z","timestamp":1554249600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100003130","name":"Fonds Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We give an improvement of the deformation method for computing the zeta function of a generic projective hypersurface over a finite field of characteristic\u00a0\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    that reduces the dependence of the complexity on\u00a0\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p\">\n                        <mml:semantics>\n                          <mml:mi>p<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">p<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    to\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"ModifyingAbove upper O With tilde left-parenthesis p Superscript 1 slash 2 Baseline right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mover>\n                                <mml:mi>O<\/mml:mi>\n                                <mml:mo stretchy=\"false\">\n                                  ~\n                                  \n                                <\/mml:mo>\n                              <\/mml:mover>\n                            <\/mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:msup>\n                              <mml:mi>p<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>1<\/mml:mn>\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mo>\/<\/mml:mo>\n                                <\/mml:mrow>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msup>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\tilde {O}(p^{1\/2})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    while remaining polynomial in the other input parameters.\n                  <\/p>","DOI":"10.1090\/mcom\/3325","type":"journal-article","created":{"date-parts":[[2017,9,13]],"date-time":"2017-09-13T10:40:34Z","timestamp":1505299234000},"page":"439-451","source":"Crossref","is-referenced-by-count":2,"title":["Computing zeta functions of generic projective hypersurfaces in larger characteristic"],"prefix":"10.1090","volume":"88","author":[{"given":"Jan","family":"Tuitman","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2018,4,3]]},"reference":[{"key":"1","unstructured":"T. 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