On the number of Diophantine \(m\)-tuples in finite fields

DOI10.1016/j.ffa.2023.102241zbMath1522.11017arXiv2301.04063MaRDI QIDQ6099004

Igor E. Shparlinski

Publication date: 19 June 2023

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.04063

zbMATH Keywords

finite fieldscharacter sumsDiophantine \(m\)-tuples

Mathematics Subject Classification ID

Quadratic and bilinear Diophantine equations (11D09) Congruences in many variables (11D79) Estimates on character sums (11L40)

Cites Work

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• \(D(-1)\) tuples in imaginary quadratic fields
• Diophantine triples and \(K3\) surfaces
• Diophantine \(m\)-tuples in finite fields and modular forms
• There are only finitely many Diophantine quintuples
• There Are Infinitely Many Rational Diophantine Sextuples
• There is no Diophantine quintuple
• Generalized Diophantine 𝑚-tuples
• Number of Points of Varieties in Finite Fields
• Diophantine tuples over $\mathbb {Z}_p$
• k-Diophantine m-tuples in finite fields
• There is no Diophantine D(−1)$D(-1)$‐quadruple

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