Titlebook: Classical Diophantine Equations; Vladimir G. Sprind?uk,Ross Talent Book 1993 Springer-Verlag Berlin Heidelberg 1993 Algebraic Number Theor

GROVE

Elizabeth’s Presence in the Jacobean Masque results. Then we proceed to a new type of equations in which at least one of the unknowns is a power of an unknown integer. Our aim is to bound the unknown exponent so as to reduce these new equations to those of the kind considered before. In this way we determine, for example, that any integral p

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https://doi.org/10.1057/9780230307261tion of polynomials. The main result asserts that under such specialisations the multiplicative structure of the numbers obtained goes some considerable way towards determining the multiplicative structure of the original polynomials. This allows one to give effective versions of Hilbert‘s irreducib

新星

Linear forms in the logarithms of algebraic numbers,mbers in different (archimedean and non-archimedean) metrics. This material will later be used in the analysis of Thue and Thue-Mahler equations. Elliptic and hyperelliptic equations, and equations of hyperelliptic type, will be analysed using direct bounds for linear forms in the logarithms of alge

debris

The Thue equation,rn as in Chapter I, to the connection between the magnitude of solutions of Thue‘s equation and rational approximation of algebraic numbers: but now our approach is the opposite of Thue‘s: we obtain bounds for the approximation as a corollary to bounds for the solutions. We arrive at an effective im

浸軟

The Thue-Mahler equation,litatively new facts, for example, that the speed of growth of the maximal prime divisor of a binary form can be bounded from below. And we can deepen the bounds for rational approximations of algebraic numbers by including the p-adic metrics. We begin by investigating the solution of the Thue equat

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Equations of hyperelliptic type, results. Then we proceed to a new type of equations in which at least one of the unknowns is a power of an unknown integer. Our aim is to bound the unknown exponent so as to reduce these new equations to those of the kind considered before. In this way we determine, for example, that any integral p

Peristalsis

The class number value problem, regulators of certain algebraic number fields related to the equation. Now we concentrate our attention on this phenomenon and relate it to the general problem of the magnitude of ideal class numbers. We show that algebraic number fields with ‘small’ regulator (hence ‘large’ class number) occur ver

squander

Reducibility of polynomials and diophantine equations,tion of polynomials. The main result asserts that under such specialisations the multiplicative structure of the numbers obtained goes some considerable way towards determining the multiplicative structure of the original polynomials. This allows one to give effective versions of Hilbert‘s irreducib