Uniform bounds for the number of solutions to Yn = f(X)

DOI10.1017/S0305004100066068zbMath0611.10009MaRDI QIDQ3751643

Joseph H. Silverman, Jan-Hendrik Evertse

Publication date: 1986

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

number of solutionsalgebraic number fieldexplicit upper boundsring of S-integersone- dimensional function field

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Units and factorization (11R27) Iwasawa theory (11R23) Higher degree equations; Fermat's equation (11D41)

Related Items (21)

Gaussian phenomena for small quadratic residues and non-residues ⋮ On the number of \(S\)-integral solutions to \(Y^m = f(X)\) ⋮ The number of elliptic curves over \(\mathbb{Q}\) with conductor \(N\) ⋮ Integral points on a certain family of elliptic curves ⋮ Divisibility of the class numbers of imaginary quadratic fields ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ Integral points on cubic twists of Mordell curves ⋮ On effective \(\epsilon\)-integrality in orbits of rational maps over function fields and multiplicative dependence ⋮ A NOTE ON SCHMIDT’S CONJECTURE ⋮ Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝 ⋮ Injectivity of the specialization homomorphism of elliptic curves ⋮ A Pair of Quadratic Fields with Class Number Divisible by 3 ⋮ On the prime factors of the iterates of the Ramanujan τ–function ⋮ ON THE NUMBER OF INTEGER POINTS ON THE ELLIPTIC CURVE y² = x³ + Ax ⋮ Unnamed Item ⋮ L'ensemble exceptionnel dans la conjecture de Szpiro ⋮ On the exponents of class groups of some families of imaginary quadratic fields ⋮ Integral points on elliptic curves and 3-torsion in class groups ⋮ Exponents of class groups and elliptic curves. ⋮ Generalized Diophantine 𝑚-tuples ⋮ Infinite families of class groups of quadratic fields with 3-rank at least one: quantitative bounds

Cites Work

• Unnamed Item
• Unnamed Item
• On \(S\)-integral solutions of the equation \(y^ m=f(x)\)
• On equations in S-units and the Thue-Mahler equation
• Finiteness theorems for abelian varieties over number fields.
• The Catalan Equation over Function Fields

This page was built for publication: Uniform bounds for the number of solutions to Yⁿ = f(X)