{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T06:41:46Z","timestamp":1776840106377,"version":"3.51.2"},"reference-count":24,"publisher":"American Mathematical Society (AMS)","issue":"270","license":[{"start":{"date-parts":[[2010,9,11]],"date-time":"2010-09-11T00:00:00Z","timestamp":1284163200000},"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 show that the modular functions\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"j Subscript 1 comma 5\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>j<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mn>5<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">j_{1,5}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"j Subscript 1 comma 6\">\n                        <mml:semantics>\n                          <mml:msub>\n                            <mml:mi>j<\/mml:mi>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mn>1<\/mml:mn>\n                              <mml:mo>,<\/mml:mo>\n                              <mml:mn>6<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msub>\n                          <mml:annotation encoding=\"application\/x-tex\">j_{1,6}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    generate function fields of the modular curves\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper X 1 left-parenthesis upper N right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>X<\/mml:mi>\n                              <mml:mn>1<\/mml:mn>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">X_1(N)<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    (\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper N equals 5 comma 6\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>N<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>5<\/mml:mn>\n                            <mml:mo>,<\/mml:mo>\n                            <mml:mn>6<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">N=5,6<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , respectively) and find some number-theoretic properties of these modular functions.\n                  <\/p>","DOI":"10.1090\/s0025-5718-09-02303-5","type":"journal-article","created":{"date-parts":[[2010,2,4]],"date-time":"2010-02-04T11:19:48Z","timestamp":1265282388000},"page":"1047-1066","source":"Crossref","is-referenced-by-count":2,"title":["Generators of function fields of the modular curves \ud835\udc4b\u2081(5) and \ud835\udc4b\u2081(6)"],"prefix":"10.1090","volume":"79","author":[{"given":"Chang","family":"Kim","sequence":"first","affiliation":[]},{"given":"Ja Kyung","family":"Koo","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2009,9,11]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1007\/BF01232032","article-title":"Monstrous moonshine and monstrous Lie superalgebras","volume":"109","author":"Borcherds, Richard E.","year":"1992","journal-title":"Invent. 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