04548nam a22005415i 4500 978-3-031-51959-8 DE-He213 20251030112100.0 cr nn 008mamaa 240527s2024 sz | s |||| 0|eng d 9783031519598 978-3-031-51959-8 10.1007/978-3-031-51959-8 doi QA241-247.5 PBH bicssc MAT022000 bisacsh PBH thema New Frontiers in Number Theory and Applications [electronic resource] / edited by Jordi Guàrdia, Nicuşor Minculete, Diana Savin, Montserrat Vela, Abdelkader Zekhnini. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024. XXIV, 446 p. 1 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Trends in Mathematics, 2297-024X 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. 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. Number theory. Number Theory. Guàrdia, Jordi. editor. edt http://id.loc.gov/vocabulary/relators/edt 77487 Minculete, Nicuşor. editor. edt http://id.loc.gov/vocabulary/relators/edt 77488 Savin, Diana. editor. edt http://id.loc.gov/vocabulary/relators/edt 77489 Vela, Montserrat. editor. edt http://id.loc.gov/vocabulary/relators/edt 77490 Zekhnini, Abdelkader. editor. edt http://id.loc.gov/vocabulary/relators/edt 77491 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031519581 Printed edition: 9783031519604 Printed edition: 9783031519611 Trends in Mathematics, 2297-024X 71516 https://doi.org/10.1007/978-3-031-51959-8 ZDB-2-SMA ZDB-2-SXMS 60149 60149