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Full Description
This contributed volume presents recent advances as well as new directions in number theory and its applications. Algebraic and analytic number theory are the main focus with chapters showing how these areas are rapidly evolving. By gathering authors from over seven countries, readers will gain an international perspective on the current state of research as well as potential avenues to explore. Specific topics covered include:
Algebraic Number Theory
Elliptic curves and Cryptography
Hopf Galois theory
Analytic and elementary number theory and applications
New Frontiers in Number Theory and Applications will appeal to researchers interested in gaining a global view of current research in number theory.
Contents
Chapter. 1. Survey Number Theoretic Transform Algorithm over a polynomial ring and its application.- Chapter. 2. On the Hilbert 2-class field towers of the layers of some cyclotomic Z2- extensions.- Chapter. 3. Some remarks on the coefficients of cyclotomic polynomials.- Chapter. 4. Partitions enumerated by self-similar sequences.- Chapter. 5. On the exact divisibility by 5 of the class number of some pure metacyclic fields.- Chapter. 6. On monogenity of certain number fields defined by a trinomial xpr + ax + b.- Chapter. 7. Irreducible Factors of a Polynomial and Extensions of Valuations.- Chapter. 8. Lengths and Class Numbers.- Chapter. 9. On Extended k-order Fibonacci and Lucas Numbers via DGC Numbers.- Chapter. 10. Generalizations of Stirling-like and Bell-like numbers.- Chapter. 11. The complex multiplication method for genus 3 curves.- Chapter. 12. An optimal Chevalley-Warning theorem over the field of two elements.- Chapter. 13. New perspectives of the power-commutator structure: coclass trees of CF-groups and related BCF-groups.- Chapter. 14. The Euler-Riemann zeta function with even arguments in terms of binomial coefficients.- Chapter. 15. Some properties of a type of entropy of an ideal and the divergence of two ideals.- Chapter. 16. A simple and self-contained proof for the Lindemann-Weierstrass theorem.- Chapter. 17. On the 2-class number of some real cyclic quartic number fields II.- Chapter. 18. On the p -isogenies of elliptic curves with multiplicative reduction over quadratic fields.- Chapter. 19. The Hopf-Galois structures of the 3 and 6-division points of the lemniscate curve.
