Number Theory I: Fundamental Problems, Ideas and Theories
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1995
|
| Schriftenreihe: | Encyclopaedia of Mathematical Sciences
49 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems (including some modern areas such as cryptography, factorization and primality testing), the central ideas of modern theories are exposed: algebraic number theory, calculations and properties of Galois groups, non-Abelian generalizations of class field theory, recursive computability and links with Diophantine equations, the arithmetic of algebraic varieties, connections with modular forms, zeta- and L-functions. The authors have tried to present the most significant results and methods of modern time. An overview of the major conjectures is also given in order to illustrate current thinking in number theory. Most of these conjectures are based on analogies between functions and numbers, and on connections with other branches of mathematics such as algebraic topology, analysis, representation theory and geometry |
| Beschreibung: | 1 Online-Ressource (V, 306 p) |
| ISBN: | 9783662080054 9783662080078 |
| ISSN: | 0938-0396 |
| DOI: | 10.1007/978-3-662-08005-4 |
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Datensatz im Suchindex
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| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-08005-4 |
| format | Electronic eBook |
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| id | DE-604.BV042423403 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662080054 9783662080078 |
| issn | 0938-0396 |
| language | English |
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| physical | 1 Online-Ressource (V, 306 p) |
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| publishDate | 1995 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Encyclopaedia of Mathematical Sciences |
| spelling | Paršin, Aleksej Nikolaevič 1942-2022 Verfasser (DE-588)172519012 aut Number Theory I Fundamental Problems, Ideas and Theories edited by A. N. Parshin, I. R. Shafarevich Berlin, Heidelberg Springer Berlin Heidelberg 1995 1 Online-Ressource (V, 306 p) txt rdacontent c rdamedia cr rdacarrier Encyclopaedia of Mathematical Sciences 49 0938-0396 This book surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems (including some modern areas such as cryptography, factorization and primality testing), the central ideas of modern theories are exposed: algebraic number theory, calculations and properties of Galois groups, non-Abelian generalizations of class field theory, recursive computability and links with Diophantine equations, the arithmetic of algebraic varieties, connections with modular forms, zeta- and L-functions. The authors have tried to present the most significant results and methods of modern time. An overview of the major conjectures is also given in order to illustrate current thinking in number theory. Most of these conjectures are based on analogies between functions and numbers, and on connections with other branches of mathematics such as algebraic topology, analysis, representation theory and geometry Mathematics Data encryption (Computer science) Geometry, algebraic Logic, Symbolic and mathematical Number theory Mathematical physics Number Theory Algebraic Geometry Mathematical Logic and Foundations Mathematical Methods in Physics Numerical and Computational Physics Data Encryption Mathematik Mathematische Physik Šafarevič, Igorʹ R. 1923-2017 Sonstige (DE-588)119280337 oth https://doi.org/10.1007/978-3-662-08005-4 Verlag Volltext |
| spellingShingle | Paršin, Aleksej Nikolaevič 1942-2022 Number Theory I Fundamental Problems, Ideas and Theories Mathematics Data encryption (Computer science) Geometry, algebraic Logic, Symbolic and mathematical Number theory Mathematical physics Number Theory Algebraic Geometry Mathematical Logic and Foundations Mathematical Methods in Physics Numerical and Computational Physics Data Encryption Mathematik Mathematische Physik |
| title | Number Theory I Fundamental Problems, Ideas and Theories |
| title_auth | Number Theory I Fundamental Problems, Ideas and Theories |
| title_exact_search | Number Theory I Fundamental Problems, Ideas and Theories |
| title_full | Number Theory I Fundamental Problems, Ideas and Theories edited by A. N. Parshin, I. R. Shafarevich |
| title_fullStr | Number Theory I Fundamental Problems, Ideas and Theories edited by A. N. Parshin, I. R. Shafarevich |
| title_full_unstemmed | Number Theory I Fundamental Problems, Ideas and Theories edited by A. N. Parshin, I. R. Shafarevich |
| title_short | Number Theory I |
| title_sort | number theory i fundamental problems ideas and theories |
| title_sub | Fundamental Problems, Ideas and Theories |
| topic | Mathematics Data encryption (Computer science) Geometry, algebraic Logic, Symbolic and mathematical Number theory Mathematical physics Number Theory Algebraic Geometry Mathematical Logic and Foundations Mathematical Methods in Physics Numerical and Computational Physics Data Encryption Mathematik Mathematische Physik |
| topic_facet | Mathematics Data encryption (Computer science) Geometry, algebraic Logic, Symbolic and mathematical Number theory Mathematical physics Number Theory Algebraic Geometry Mathematical Logic and Foundations Mathematical Methods in Physics Numerical and Computational Physics Data Encryption Mathematik Mathematische Physik |
| url | https://doi.org/10.1007/978-3-662-08005-4 |
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