Squares in arithmetic progressions

DOI10.1215/S0012-7094-92-06612-9zbMath0771.11034OpenAlexW2071628284MaRDI QIDQ1196391

Andrew Granville, Enrico Bombieri, János Pintz

Publication date: 14 December 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-92-06612-9

zbMATH Keywords

Mordell-Weil grouparithmetic progressionnumber of rational pointsexplicit upper boundFaltings' theoremnumber of squares

Mathematics Subject Classification ID

Rational points (14G05) Distribution of integers in special residue classes (11N69) Distribution of integers with specified multiplicative constraints (11N25) Arithmetic progressions (11B25)

Related Items (16)

Discrete fractional integrals, lattice points on short arcs, and diophantine approximation ⋮ On the Chowla and twin primes conjectures over \(\mathbb{F}_q[T\)] ⋮ Squares in Arithmetic Progressions and Infinitely Many Primes ⋮ Four rational squares in arithmetic progressions and a family of elliptic curves with positive Mordell-Weil rank ⋮ Five squares in arithmetic progression over quadratic fields ⋮ On problems of Erdős and Rudin. ⋮ Squares in arithmetic progression over number fields ⋮ Sums and products along sparse graphs ⋮ On a conjecture of Rudin on squares in arithmetic progressions ⋮ Shifted products that are coprime pure powers ⋮ Powers in arithmetic progressions ⋮ On the number of times a root of \(f(n,x)=0\) generates a field containing a given number field ⋮ On arithmetic progressions on Edwards curves ⋮ Uniform bounds for the number of powers in arithmetic progressions ⋮ COMPLEXITY OF SHORT GENERATING FUNCTIONS ⋮ The Uniformity Conjecture in Additive Combinatorics

Cites Work

• Number theory III: Diophantine geometry
• On the number of rational points of a plane algebraic curve
• Diophantine Equations with Special Reference To Elliptic Curves
• The Jacobian Variety of an Algebraic Curve
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