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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. --- Cryptography. --- Number Theory --- Nombres, Théorie des --- Théorie des nombres --- Cryptography --- Number theory --- #TELE:SISTA --- 519.72 --- 519.72 Information theory: mathematical aspects --- Information theory: mathematical aspects --- Number study --- Numbers, Theory of --- Algebra --- Cryptanalysis --- Cryptology --- Secret writing --- Steganography --- Signs and symbols --- Symbolism --- Writing --- Ciphers --- Data encryption (Computer science) --- cryptografie --- Cryptographie --- Nombres, Théorie des. --- Cryptographie. --- Nombres, Théorie des.

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This introduction to recent work in p-adic analysis and number theory will make accessible to a relatively general audience the efforts of a number of mathematicians over the last five years. After reviewing the basics (the construction of p-adic numbers and the p-adic analog of the complex number field, power series and Newton polygons), the author develops the properties of p-adic Dirichlet L-series using p-adic measures and integration. p-adic gamma functions are introduced, and their relationship to L-series is explored. Analogies with the corresponding complex analytic case are stressed. Then a formula for Gauss sums in terms of the p-adic gamma function is proved using the cohomology of Fermat and Artin-Schreier curves. Graduate students and research workers in number theory, algebraic geometry and parts of algebra and analysis will welcome this account of current research.

p-adic analysis. --- Analysis, p-adic --- Algebra --- Calculus --- Geometry, Algebraic --- p-adic analysis --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- 511.6 --- 511.6 Algebraic number fields --- Algebraic number fields --- P-adic analysis. --- Number theory

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Functional analysis --- Number theory --- p-adic analysis --- p-adic numbers --- Functions, Zeta --- #WWIS:d.d. Prof. L. Bouckaert/ALTO --- 511 --- Zeta functions --- Numbers, p-adic --- Analysis, p-adic --- Algebra --- Calculus --- Geometry, Algebraic --- Functions, Zeta. --- p-adic analysis. --- p-adic numbers. --- 511 Number theory --- P-adic analysis. --- P-adic numbers.