The Paley graph conjecture and Diophantine \(m\)-tuples

DOI10.1016/j.jcta.2019.105155zbMath1428.05302OpenAlexW2979819925WikidataQ123142292 ScholiaQ123142292MaRDI QIDQ2010648

Ahmet M. Güloğlu, M. Ram Murty

Publication date: 27 November 2019

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2019.105155

zbMATH Keywords

Diophantine \(m\)-tuplesGallagher's sievePaley graph conjectureVinogradov inequality

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Quadratic and bilinear Diophantine equations (11D09) Counting solutions of Diophantine equations (11D45) Graph theory (05C99)

Related Items

On the restricted isometry property of the Paley matrix, Generalized Diophantine 𝑚-tuples

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a question of Davenport and Lewis and new character sum bounds in finite fields
• On \(k\)-triad sequences
• Explicit estimates of some functions over primes
• On generalizations of a problem of Diophantus
• On double sums with multiplicative characters
• Sums of multiplicative characters with additive convolutions
• Shifted products that are coprime pure powers
• On a problem of Diophantus
• On the size of Diophantine m-tuples
• On Some Applications of Diophantine Approximations
• A Random Model for the Paley Graph
• Estimates for Character Sums
• Sets in Which xy + k is Always a Square
• Unbiased Bits from Sources of Weak Randomness and Probabilistic Communication Complexity
• Estimation de la fonction de Tchebychef θ sur le k-ième nombre premier et grandes valeurs de la fonction ω(n) nombre de diviseurs premiers de n
• Generalization of a problem of Diophantus
• On Diophantine quintuples
• There are only finitely many Diophantine quintuples
• There is no Diophantine quintuple
• Bounds for the size of sets with the property D(n)
• On shifted products which are powers
• Diophantine m-tuples with the property D(n)
• Some rational Diophantine sextuples
• On powers in shifted products
• Linear forms in the logarithms of algebraic numbers (IV)
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²
• Uniformity of rational points