Character sums with exponential functions and their applications /

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The theme of this book is the distribution of integer powers modulo a prime number. It provides numerous new links between number theory and computer science as well as other areas of mathematics. Applications include (but are not limited to) complexity theory, random number generation, cryptography...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Koni͡agin, S. V. (Sergeĭ Vladimirovich)
Otros Autores: Shparlinski, Igor E.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, 1999.
Colección:Cambridge tracts in mathematics ; 136.
Temas:
Exponential sums.
Sommes exponentielles.
MATHEMATICS > Number Theory.
Exponential sums
Acceso en línea:Texto completo
Tabla de Contenidos:
  • pt. 1. Preliminaries
  • 1. Introduction
  • 2. Notation and Auxiliary Results
  • pt. 2. Bounds of Character Sums
  • 3. Bounds of Long Character Sums
  • 4. Bounds of Short Character Sums
  • 5. Bounds of Character Sums for Almost All Moduli
  • 6. Bounds of Gaussian Sums
  • pt. 3. Multiplicative Translations of Sets
  • 7. Multiplicative Translations of Subgroups of F*[subscript p]
  • 8. Multiplicative Translations of Arbitrary Sets Modulo p
  • pt. 4. Applications to Algebraic Number Fields
  • 9. Representatives of Residue Classes
  • 10. Cyclotomic Fields and Gaussian Periods
  • pt. 5. Applications to Pseudo-Random Number Generators
  • 11. Prediction of Pseudo-Random Number Generators
  • 12. Congruential Pseudo-Random Number Generators
  • pt. 6. Applications to Finite Fields
  • 13. Small mth Roots Modulo p
  • 14. Supersingular Hyperelliptic Curves
  • 15. Distribution of Powers of Primitive Roots
  • pt. 7. Applications to Coding Theory and Combinatorics
  • 16. Difference Sets in V[subscript p]
  • 17. Dimension of BCH Codes
  • 18. An Enumeration Problem in Finite Fields.

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