Number Theory. Volume I, Tools and Diophantine Equations
The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation...
Guardat en:
| Autor principal: | |
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| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2007. |
| Col·lecció: | Graduate Texts in Mathematics
239 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 672 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Number theory, Volume I, Tools and diophantine equations, Henri Cohen, 2007, New York, Springer, 1 vol. (XXIII-650 p.), Graduate Texts in Mathematics, 978-0-387-49922-2 • Number theory, Volume I, Tools and diophantine equations, Henri Cohen, 2007, New York, Springer, 1 vol. (XXIII-650 p.), Graduate Texts in Mathematics, 978-0-387-49922-2 • Computer simulation studies in condensed-matter physics, V, Proceedings of the fifth workshop, Athens, GA, USA, February 17-21, 1992, D.P. Landau, K.K. Mon, H.-B. Schüttler, eds, Berlin, Springer-Verlag, 1993, 1 vol. (VIII-197 p.), Springer proceedings in physics, 0-387-56474-8 • Number theory, Volume I, Tools and diophantine equations, Henri Cohen, 2007, New York, Springer, 1 vol. (XXIII-650 p.), Graduate Texts in Mathematics, 978-0-387-49922-2 |
| Sumari: | The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects. The first is the local aspect: one can do analysis in p-adic fields, and here the author starts by looking at solutions in finite fields, then proceeds to lift these solutions to local solutions using Hensel lifting. The second is the global aspect: the use of number fields, and in particular of class groups and unit groups. This classical subject is here illustrated through a wide range of examples. The third aspect deals with specific classes of equations, and in particular the general and Diophantine study of elliptic curves, including 2 and 3-descent and the Heegner point method. These subjects form the first two parts, forming Volume I. The study of Bernoulli numbers, the gamma function, and zeta and L-functions, and of p-adic analogues is treated at length in the third part of the book, including many interesting and original applications. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five chapters on these techniques forming the fourth part, which together with the third part forms Volume II. These chapters were written by Yann Bugeaud, Guillaume Hanrot, Maurice Mignotte, Sylvain Duquesne, Samir Siksek, and the author, and contain material on the use of Galois representations, points on higher-genus curves, the superfermat equation, Mihailescu's proof of Catalan's Conjecture, and applications of linear forms in logarithms. The book contains 530 exercises of varying difficulty from immediate consequences of the main text to research problems, and contain many important additional results. |
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| Descripció de l’ítem: | L'impression du document génère 672 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografia: | Bibliogr. Index |
| ISBN: | 9780387499239 |
| ISSN: | 2197-5612 |
| Accés: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |