{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:09:44Z","timestamp":1776784184583,"version":"3.51.2"},"reference-count":6,"publisher":"American Mathematical Society (AMS)","issue":"250","license":[{"start":{"date-parts":[[2005,10,29]],"date-time":"2005-10-29T00:00:00Z","timestamp":1130544000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We present the computation modulo\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"p squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>p<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">p^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and explicit formulas for the unique isogeny covariant differential modular form of order one and weight\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"chi Subscript negative p minus 1 comma negative p\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>\n                              \u03c7\n                              \n                            <\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:mi>p<\/mml:mi>\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:mi>p<\/mml:mi>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\chi _{-p-1,-p}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    called\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"f Subscript normal j normal e normal t\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>f<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"normal\">j<\/mml:mi>\n                                <mml:mi mathvariant=\"normal\">e<\/mml:mi>\n                                <mml:mi mathvariant=\"normal\">t<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">f_{\\mathrm {jet}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , an isogeny covariant differential modular form of order two and weight\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"chi Subscript minus p squared minus p comma negative 1 comma negative 1\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>\n                              \u03c7\n                              \n                            <\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:msup>\n                                <mml:mi>p<\/mml:mi>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:msup>\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:mi>p<\/mml:mi>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\chi _{-p^2-p,-1,-1}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    denoted by\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"f Subscript normal j normal e normal t Baseline h Subscript normal j normal e normal t\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>f<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mi mathvariant=\"normal\">j<\/mml:mi>\n                                  <mml:mi mathvariant=\"normal\">e<\/mml:mi>\n                                  <mml:mi mathvariant=\"normal\">t<\/mml:mi>\n                                <\/mml:mrow>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:msub>\n                              <mml:mi>h<\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                  <mml:mi mathvariant=\"normal\">j<\/mml:mi>\n                                  <mml:mi mathvariant=\"normal\">e<\/mml:mi>\n                                  <mml:mi mathvariant=\"normal\">t<\/mml:mi>\n                                <\/mml:mrow>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">f_{\\mathrm {jet}}h_{\\mathrm {jet}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , and an isogeny covariant differential modular form\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h Subscript normal j normal e normal t\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi mathvariant=\"normal\">j<\/mml:mi>\n                                <mml:mi mathvariant=\"normal\">e<\/mml:mi>\n                                <mml:mi mathvariant=\"normal\">t<\/mml:mi>\n                              <\/mml:mrow>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">h_{\\mathrm {jet}}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    of order two and weight\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"chi Subscript 1 minus p squared comma 0 comma negative 1\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>\n                              \u03c7\n                              \n                            <\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:msup>\n                                <mml:mi>p<\/mml:mi>\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:msup>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mn>0<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mo>\n                                \u2212\n                                \n                              <\/mml:mo>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">\\chi _{1-p^2,0,-1}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-04-01721-1","type":"journal-article","created":{"date-parts":[[2005,1,14]],"date-time":"2005-01-14T14:25:09Z","timestamp":1105712709000},"page":"905-926","source":"Crossref","is-referenced-by-count":0,"title":["Computing isogeny covariant differential modular forms"],"prefix":"10.1090","volume":"74","author":[{"given":"Chris","family":"Hurlburt","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2004,10,29]]},"reference":[{"issue":"28","key":"1","doi-asserted-by":"publisher","first-page":"1457","DOI":"10.1155\/S1073792802110063","article-title":"Siegel differential modular forms","author":"Barcau, Mugurel","year":"2002","journal-title":"Int. Math. Res. Not.","ISSN":"https:\/\/id.crossref.org\/issn\/1073-7928","issn-type":"print"},{"key":"2","unstructured":"A. Buium, Geometry of Fermat Adeles, Preprint, 1999."},{"key":"3","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1515\/crll.2000.024","article-title":"Differential modular forms","volume":"520","author":"Buium, Alexandru","year":"2000","journal-title":"J. Reine Angew. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0075-4102","issn-type":"print"},{"key":"4","unstructured":"\\bysame, Arithmetic Differential Invariants, In preparation, 2003."},{"issue":"1","key":"5","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1023\/A:1017536003747","article-title":"Isogeny covariant differential modular forms modulo \ud835\udc5d","volume":"128","author":"Hurlburt, Chris","year":"2001","journal-title":"Compositio Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-437X","issn-type":"print"},{"key":"6","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1920-8","volume-title":"The arithmetic of elliptic curves","volume":"106","author":"Silverman, Joseph H.","year":"1986","ISBN":"https:\/\/id.crossref.org\/isbn\/0387962034"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2005-74-250\/S0025-5718-04-01721-1\/S0025-5718-04-01721-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-250\/S0025-5718-04-01721-1\/S0025-5718-04-01721-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:06:06Z","timestamp":1776780366000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2005-74-250\/S0025-5718-04-01721-1\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10,29]]},"references-count":6,"journal-issue":{"issue":"250","published-print":{"date-parts":[[2005,4]]}},"alternative-id":["S0025-5718-04-01721-1"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-04-01721-1","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2004,10,29]]}}}