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Number theory --- Curves, Elliptic --- Forms, Modular --- Courbes elliptiques --- Formes modulaires --- Théorie des nombres --- Number Theory --- 511.33 --- Number study --- Numbers, Theory of --- Algebra --- Modular forms --- Forms (Mathematics) --- Elliptic curves --- Curves, Algebraic --- Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- 511.33 Analytical and multiplicative number theory. Asymptotics. Sieves etc. --- Théorie des nombres --- Analytical and multiplicative number theory. Asymptotics. Sieves etc

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Number theory --- 519.72 --- 512.742 --- 511 --- 511 Number theory --- 512.742 Abelian varieties and schemes. Elliptic curves --- Abelian varieties and schemes. Elliptic curves --- 519.72 Information theory: mathematical aspects --- Information theory: mathematical aspects --- Number study --- Numbers, Theory of --- Algebra --- Cryptography --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- cryptografie --- Cryptography. --- Cryptographie --- Théorie des nombres --- Number theory.

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These autobiographical memoirs of Neal Koblitz, coinventor of one of the two most popular forms of encryption and digital signature, cover many topics besides his own personal career in mathematics and cryptography - travels to the Soviet Union, Latin America, Vietnam and elsewhere, political activism, and academic controversies relating to math education, the C. P. Snow two-culture problem, and mistreatment of women in academia. The stories speak for themselves and reflect the experiences of a student and later a scientist caught up in the tumultuous events of his generation.

Mathematics. --- History of Mathematics. --- Number Theory. --- Data Encryption. --- Data Structures, Cryptology and Information Theory. --- Data structures (Computer science). --- Data encryption (Computer science). --- Mathematics_$xHistory. --- Number theory. --- Mathématiques --- Structures de données (Informatique) --- Chiffrement (Informatique) --- Théorie des nombres --- Koblitz, Neal. --- Mathematicians --- World politics --- Mathematics - General --- Mathematics --- Physical Sciences & Mathematics --- Koblitz, Neal, --- Travel. --- Koblit︠s︡, N., --- Koblitz, Neal I. --- History. --- History of Mathematical Sciences.

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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.

Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Nombres transcendants