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Number theory IV : transcendental numbers

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  • "Number theory IV"
  • "Teoriâ čisel"
  • "Introduction to number theory"@en
  • "Transcendental numbers"@en
  • "Transcendental numbers"
  • "Fundamental problems, ideas and theories"
  • "Number theory I"

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  • "This book is a survey of the most important directions of research in transcendental number theory. The central topics in this theory include proofs of irrationality and transcendence of various numbers, especially those that arise as the values of special functions. Questions of this sort go back to ancient times. An example is the old problem of squaring the circle, which Lindemann showed to be impossible in 1882, when he proved that $Öpi$ is a transcendental number. Euler's conjecture that the logarithm of an algebraic number to an algebraic base is transcendental was included in Hilbert's famous list of open problems; this conjecture was proved by Gel'fond and Schneider in 1934. A more recent result was ApÖ'ery's surprising proof of the irrationality of $Özeta(3)$ in 1979. The quantitative aspects of the theory have important applications to the study of Diophantine equations and other areas of number theory. For a reader interested in different branches of number theory, this monograph provides both an overview of the central ideas and techniques of transcendental number theory, and also a guide to the most important results."
  • "This book surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems (including some modern areas such as cryptography, factorization and primality testing), the central ideas of modern theories are exposed: algebraic number theory, calculations and properties of Galois groups, non-Abelian generalizations of class field theory, recursive computability and links with Diophantine equations, the arithmetic of algebraic varieties, connections with modular forms, zeta- and L-functions. The authors have tried to present the most significant results and methods of modern time. An overview of the major conjectures is also given in order to illustrate current thinking in number theory. Most of these conjectures are based on analogies between functions and numbers, and on connections with other branches of mathematics such as algebraic topology, analysis, representation theory and geometry."

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  • "Electronic books"

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  • "Number theory. I, Fundamental problems, ideas and theories"
  • "Number Theory I Fundamental Problems, Ideas and Theories"
  • "Number theory 4. : transcendental numbers"
  • "Number theory IV : transcendental numbers"
  • "Number theory IV : transcendental numbers"@en
  • "Number theory. 4, Transcendental numbers"
  • "Fundamental problems, ideas and theories : A.N. Parshin ... (eds.)"
  • "Number theory. 1 : fundamental problems, ideas and theories"
  • "Teoria cisel"
  • "Teoriya chisel"
  • "Teorija čisel"
  • "Number theory I fundamental problems, ideas and theories"@en
  • "Fundamental problems, ideas and theories"
  • "Number Theory"
  • "Number theory. 1, Fundamental problems, ideas and theories / A. N. Parshin ... (eds.) - 1995"
  • "Number theory : fundamental problems, ideas and theories"
  • "Teoriya chisel 1"
  • "Number theory"@en
  • "Number theory"
  • "Number theory I : fundamental problems, ideas and theories"@en
  • "Number theory I : fundamental problems, ideas and theories"
  • "Fundamental problems, ideas, and theories"
  • "Number theory 1. : fundamental problems, ideas and theories"
  • "Number Theory IV Transcendental Numbers"
  • "Number theory. IV, Transcendental numbers"@en
  • "Number theory. IV, Transcendental numbers"
  • "Number theory. 4, Transcendental numbers / A.N. Parshin ...(eds.)"
  • "Number Theory I : Fundamental Problems, Ideas and Theories"
  • "Number theory. 1, Fundamental problems, ideas and theories"
  • "Number theory 4. Transcendental numbers / A. N. Parshin ; I. R. Shafarevich (ed.)"
  • "Number theory. I, fundamental problems, ideas and theories"@en
  • "Itogi nauki i tekhniki, Sovremennye problemy matematiki, fundamental'nye napravleniya, Vol. 49, Teoria chisel 1"
  • "Number theory. 1. Fundamental problems, ideas and theories"

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