On existence of primitive pairs (ξ plus ξ-1, f(ξ)) with arbitrary traces

被引：0
|
作者：
Shukla, Aastha [1 ]
Tiwari, Shailesh Kumar [1 ]
机构：
[1] Indian Inst Technol Patna, Dept Math, Patna 801106, Bihar, India
来源：
COMMUNICATIONS IN ALGEBRA | 2024年
关键词：
Field extension; finite field; primitive element; sieve inequality; ELEMENTS; FIELDS;
D O I：
10.1080/00927872.2024.2444641
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let Fqn be a finite extension of the finite field Fq of degree n, where q is a prime power and n is a positive integer. Suppose a,b is an element of Fq. In this article we search for pairs (q, n) such that there exists a primitive pair (xi+xi-1,f(xi)) with TrFqn/Fq(xi)=a and TrFqn/Fq(xi-1)=b, where xi is a non-zero element of Fqn and f is any non-exceptional rational function in Fqn(x).
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页数：13
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