{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:48:38Z","timestamp":1776721718810,"version":"3.51.2"},"reference-count":12,"publisher":"American Mathematical Society (AMS)","issue":"213","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    For\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n greater-than-or-equal-to 7\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                            <mml:mo>\n                              \u2265\n                              \n                            <\/mml:mo>\n                            <mml:mn>7<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">n\\ge 7<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , we prove that there always exists a primitive polynomial of degree\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"n\">\n                        <mml:semantics>\n                          <mml:mi>n<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    over a finite field\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper F Subscript q Baseline left-parenthesis q o d d right-parenthesis\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi>F<\/mml:mi>\n                              <mml:mi>q<\/mml:mi>\n                            <\/mml:msub>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>q<\/mml:mi>\n                            <mml:mi>odd<\/mml:mi>\n                            <mml:mo stretchy=\"false\">)<\/mml:mo>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">F_q (q \\operatorname {odd})<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with the first and second coefficients prescribed in advance.\n                  <\/p>","DOI":"10.1090\/s0025-5718-96-00663-1","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"331-340","source":"Crossref","is-referenced-by-count":17,"title":["The coefficients of primitive polynomials over finite fields"],"prefix":"10.1090","volume":"65","author":[{"given":"Wen Bao","family":"Han","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"S. D. Cohen, Primitive elements and polynomials with arbitrary traces, Discrete Math. (2) 83 (1990), 1\u20137.","DOI":"10.1016\/0012-365X(90)90215-4"},{"key":"2","unstructured":"\\bysame, Primitive elements and polynomials: existence results, Lecture Notes in Pure and Appl. Math., vol. 141, edited by G. L. Mullen and P. J. Shiue, Marcel Dekker, New York, 1992, pp. 43\u201355."},{"key":"3","doi-asserted-by":"crossref","unstructured":"H. Davenport, Bases for finite fields, J. London Math. Soc. 43 (1968), 21\u201339.","DOI":"10.1112\/jlms\/s1-43.1.21"},{"key":"4","unstructured":"W.-B. Han, Primitive roots and linearized polynomials, Adv. in Math. (China) 22 (1994), 460\u2013462."},{"key":"5","doi-asserted-by":"crossref","unstructured":"T. Hansen and G. L. Mullen, Primitive polynomials over finite fields Math. Comp. 59 (1992), 639\u2013643.","DOI":"10.1090\/S0025-5718-1992-1134730-7"},{"key":"6","doi-asserted-by":"crossref","unstructured":"D. Jungnickel and S. A. Vanstone, On primitive polynomials over finite fields, J. Algebra 124 (1989), 337\u2013353.","DOI":"10.1016\/0021-8693(89)90136-1"},{"key":"7","unstructured":"R. Lidl and H. Niederreiter, Finite fields, Addison-Wesley, Reading, MA, 1983."},{"key":"8","doi-asserted-by":"crossref","unstructured":"H. W. Lenstra and R. J. Schoof, Primitive normal bases for finite fields, Math. Comp. 48 (1987), 217\u2013232.","DOI":"10.1090\/S0025-5718-1987-0866111-3"},{"key":"9","doi-asserted-by":"crossref","unstructured":"O. Moreno, On the existence of a primitive quadratic trace 1 over GF(j^{g}), J. Combin. Theory Ser. A 51 (1989), 104\u2013110.","DOI":"10.1016\/0097-3165(89)90080-0"},{"key":"10","doi-asserted-by":"crossref","unstructured":"W. M. Schmidt, Equations over finite fields; an elementary approach, Lecture Notes in Math., vol. 536, Springer-Verlag, Berlin and New York, 1976.","DOI":"10.1007\/BFb0080437"},{"key":"11","unstructured":"Q. Sun and W.-B. Han, The absolute trace function and primitive roots in finite fields (in Chinese), Chinese Ann. Math. Ser. A 11 (1990), 202\u2013205."},{"key":"12","unstructured":"\\bysame, Improvement of Weil exponential sums and its application, preprint."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1996-65-213\/S0025-5718-96-00663-1\/S0025-5718-96-00663-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-213\/S0025-5718-96-00663-1\/S0025-5718-96-00663-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:02:24Z","timestamp":1776718944000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1996-65-213\/S0025-5718-96-00663-1\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996]]},"references-count":12,"journal-issue":{"issue":"213","published-print":{"date-parts":[[1996,1]]}},"alternative-id":["S0025-5718-96-00663-1"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-96-00663-1","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":[[1996]]}}}