Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 71, No. 2, pp. 555-562, 2021

Sidon basis in polynomial rings over finite fields

Wentang Kuo, Shuntaro Yamagishi

Received December 21, 2019. Published online September 24, 2020.

Abstract: Let $\mathbb{F}_q[t]$ denote the polynomial ring over $\mathbb{F}_q$, the finite field of $q$ elements. Suppose the characteristic of $\mathbb{F}_q$ is not $2$ or $3$. We prove that there exist infinitely many $N \in\mathbb{N}$ such that the set $\{ f \in\mathbb{F}_q[t] \colon\deg f < N \}$ contains a Sidon set which is an additive basis of order $3$.

Keywords: Sidon set; additive basis; polynomial rings over finite fields

Classification MSC: 11K31, 11B83, 11T55

DOI: 10.21136/CMJ.2020.0543-19

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Wentang Kuo, Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, ON N2L 3G1, Canada, e-mail: wtkuo@uwaterloo.ca; Shuntaro Yamagishi (corresponding author), Mathematical Institute, Utrecht University, Budapestlaan 6, 3584 CD Utrecht, The Netherlands, e-mail: s.yamagis@uu.nl

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