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Mathematics > Number Theory

arXiv:1412.7373 (math)
[Submitted on 20 Dec 2014]

Title:On primitive elements in finite fields of low characteristic

Authors:Abhishek Bhowmick, Thái Hoàng Lê
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Abstract:We discuss the problem of constructing a small subset of a finite field containing primitive elements of the field. Given a finite field, $\mathbb{F}_{q^n}$, small $q$ and large $n$, we show that the set of all low degree polynomials contains the expected number of primitive elements.
The main theorem we prove is a bound for character sums over short intervals in function fields. Our result is unconditional and slightly better than what is known (conditionally under GRH) in the integer case and might be of independent interest.
Subjects: Number Theory (math.NT); Computational Complexity (cs.CC)
MSC classes: 11Lxx
ACM classes: G.2
Cite as: arXiv:1412.7373 [math.NT]
  (or arXiv:1412.7373v1 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1412.7373

Submission history

From: Abhishek Bhowmick [view email]
[v1] Sat, 20 Dec 2014 05:05:53 UTC (11 KB)
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