Primitive values of rational functions at primitive elements of a finite field

DOI10.1016/j.jnt.2020.09.017zbMath1468.11240arXiv1909.13074OpenAlexW3096018630WikidataQ114157164 ScholiaQ114157164MaRDI QIDQ2212632

Hariom Sharma, Stephen D. Cohen, Rajendra K. Sharma

Publication date: 24 November 2020

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.13074

zbMATH Keywords

charactersfinite fieldsprimitive element

Mathematics Subject Classification ID

Exponential sums (11T23) Finite fields (field-theoretic aspects) (12E20) Structure theory for finite fields and commutative rings (number-theoretic aspects) (11T30)

Related Items (7)

On the existence of primitive normal elements of rational form over finite fields of even characteristic ⋮ On the existence of pairs of primitive and normal elements over finite fields ⋮ Primitive normal values of rational functions over finite fields ⋮ The number of rational points of a class of superelliptic curves ⋮ Unnamed Item ⋮ Existence of primitive normal pairs with one prescribed trace over finite fields ⋮ On special pairs of primitive elements over a finite field

Uses Software

• GAP

Cites Work

• Pairs of primitive elements in fields of even order
• On the existence of some specific elements in finite fields of characteristic 2
• Using Stepanov's method for exponential sums involving rational functions
• Existence of pair of primitive elements over finite fields of characteristic 2
• Linear combinations of primitive elements of a finite field
• Primitive element pairs with one prescribed trace over a finite field
• Existence of some special primitive normal elements over finite fields
• The strong primitive normal basis theorem
• THE PRIMITIVE NORMAL BASIS THEOREM – WITHOUT A COMPUTER
• Primitive values of quadratic polynomials in a finite field
• Consecutive Primitive Roots in a Finite Field
• A proof of the conjecture of Cohen and Mullen on sums of primitive roots
• Pair of primitive elements with prescribed traces over finite fields
• On Some Exponential Sums

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