AN EFFECTIVE BOUND FOR GENERALISED DIOPHANTINE m-TUPLES

DOI10.1017/s0004972723001077OpenAlexW4388419403MaRDI QIDQ6124023

Unnamed Author, Anup B. Dixit, Unnamed Author

Publication date: 9 April 2024

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0004972723001077

zbMATH Keywords

Diophantine \(m\)-tuplesgap principleGallagher's sievequantitative Roth's theorem

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Applications of sieve methods (11N36) Diophantine equations in many variables (11D72)

Cites Work

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• Explicit bounds for primes in arithmetic progressions
• Finiteness theorems for abelian varieties over number fields.
• On a problem of Diophantus
• On the size of sets whose elements have perfect power $n$-shifted products
• There are only finitely many Diophantine quintuples
• On a problem of Diophantus for higher powers
• There is no Diophantine quintuple
• Bounds for the size of sets with the property D(n)
• Generalized Diophantine 𝑚-tuples
• Diophantine m-tuples with the property D(n)
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
• A larger sieve
• On the quantitative subspace theorem

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