{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T22:40:02Z","timestamp":1751064002075,"version":"3.41.0"},"reference-count":0,"publisher":"Combinatorial Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Ars Comb."],"published-print":{"date-parts":[[2025,6,28]]},"abstract":"<jats:p>&lt;p&gt;Let &lt;span class=\"math inline\"&gt;\\(q\\)&lt;\/span&gt; be a positive integral power of some prime &lt;span class=\"math inline\"&gt;\\(p\\)&lt;\/span&gt; and &lt;span class=\"math inline\"&gt;\\(\\mathbb{F}_{q^m}\\)&lt;\/span&gt; be a finite field with &lt;span class=\"math inline\"&gt;\\(q^m\\)&lt;\/span&gt; elements for some &lt;span class=\"math inline\"&gt;\\(m \\in \\mathbb{N}\\)&lt;\/span&gt;. Here we establish a sufficient condition for the existence of primitive normal pairs of the type &lt;span class=\"math inline\"&gt;\\((\\epsilon, f(\\epsilon))\\)&lt;\/span&gt; in &lt;span class=\"math inline\"&gt;\\(\\mathbb{F}_{q^m}\\)&lt;\/span&gt; over &lt;span class=\"math inline\"&gt;\\(\\mathbb{F}_{q}\\)&lt;\/span&gt; with two prescribed traces, &lt;span class=\"math inline\"&gt;\\(\\text{Tr}_{{\\mathbb{F}_{q^m}}\/{\\mathbb{F}_q}}(\\epsilon)=a\\)&lt;\/span&gt; and &lt;span class=\"math inline\"&gt;\\(\\text{Tr}_{{\\mathbb{F}_{q^m}}\/{\\mathbb{F}_q}}(f(\\epsilon))=b\\)&lt;\/span&gt;, where &lt;span class=\"math inline\"&gt;\\(f(x) \\in \\mathbb{F}_{q^m}(x)\\)&lt;\/span&gt; is a rational function with some restrictions and &lt;span class=\"math inline\"&gt;\\(a, b \\in \\mathbb{F}^*_q\\)&lt;\/span&gt;. Furthermore, for &lt;span class=\"math inline\"&gt;\\(q=5^k\\)&lt;\/span&gt;, &lt;span class=\"math inline\"&gt;\\(m \\geq 9\\)&lt;\/span&gt; and rational functions with degree sum 4, we explicitly find at most 13 fields in which the desired pair may not exist.&lt;\/p&gt;<\/jats:p>","DOI":"10.61091\/ars163-05","type":"journal-article","created":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T22:01:43Z","timestamp":1751061703000},"page":"69-82","source":"Crossref","is-referenced-by-count":0,"title":["Primitive normal pairs with prescribed traces over finite fields"],"prefix":"10.61091","volume":"163","author":[{"name":"Department of Mathematical Sciences, Tezpur University, Tezpur, Assam, 784028, India","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shikhamoni","family":"Nath","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arpan Chandra","family":"Mazumder","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematical Sciences, Tezpur University, Tezpur, Assam, 784028, India","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dhiren Kumar","family":"Basnet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Department of Mathematical Sciences, Tezpur University, Tezpur, Assam, 784028, India","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"39747","published-online":{"date-parts":[[2025,6,28]]},"container-title":["Ars Combinatoria"],"original-title":[],"deposited":{"date-parts":[[2025,6,27]],"date-time":"2025-06-27T22:01:45Z","timestamp":1751061705000},"score":1,"resource":{"primary":{"URL":"https:\/\/combinatorialpress.com\/ars-articles\/volume-163\/primitive-normal-pairs-with-prescribed-traces-over-finite-fields\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,28]]},"references-count":0,"URL":"https:\/\/doi.org\/10.61091\/ars163-05","relation":{},"ISSN":["0381-7032","2817-5204"],"issn-type":[{"value":"0381-7032","type":"print"},{"value":"2817-5204","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,28]]}}}