Number theory IV: Transcendental numbers. Edited by A. N. Parshin, I. R. Shafarevich and R. V. Gamkrelidze. Transl. from the Russian by Neal Koblitz

zbMath0885.11004MaRDI QIDQ1370789

N. I. Fel'dman, Yuri V. Nesterenko

Publication date: 27 October 1997

Published in: Encyclopaedia of Mathematical Sciences (Search for Journal in Brave)

zbMATH Keywords

exponential functionelimination theoryPadé approximationThue-Mahler equations\(G\)-functionselliptic functionscontinued fractionstranscendence measuresalgebraic independencelinear forms in two logarithms\(abc\) conjectureBessel's functionsHilbert's Nullstellensatztranscendental numbersCatalan's equationGelfond's methodirrationality measuresapproximation of algebraic numbersHilbert's problemChow formsKummer's functionshypergeometric \(E\)-functionseffective constructionsgood diophantine approximationshyperelliptic diophantine equationsnumber of solutions of diophantine equations

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Algebraic independence; Gel'fond's method (11J85) Measures of irrationality and of transcendence (11J82) Diophantine inequalities (11J25) Transcendence (general theory) (11J81) Linear forms in logarithms; Baker's method (11J86) Transcendence theory of elliptic and abelian functions (11J89) Approximation to algebraic numbers (11J68)

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