Exercises in Number Theory
Seiten
2010
|
Softcover reprint of hardcover 1st ed. 1984
Springer-Verlag New York Inc.
978-1-4419-3071-2 (ISBN)
Springer-Verlag New York Inc.
978-1-4419-3071-2 (ISBN)
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After an eclipse of some 50 years, Number Theory, that is to say the study of the properties of the integers, has regained in France a vitality worthy of its distinguished past. They have drawn these exercises from their own work, from the work of their associated research groups as well as from published work.
After an eclipse of some 50 years, Number Theory, that is to say the study of the properties of the integers, has regained in France a vitality worthy of its distinguished past. More 'and more researchers have been attracted by problems which, though it is possible to express in simple statements, whose solutions require all their ingenuity and talent. In so doing, their work enriches the whole of mathematics with new and fertile methods. To be in a position to tackle these problems, it is neces sary to be familiar with many specific aspects of number theory. These are very different from those encountered in analysis or geometry. The necessary know-how can only be acquired by study ing and solving numerous problems. Now it is very easy to form ulate problems whose solutions, while sometimes obvious, more often go beyond current methods. Moreover, there is no doubt that, even more than in other disciplines, in mathematics one must have exercises available whose solutions are accessible. This is the objective realised by this work. It is the collab orative work of several successful young number theorists. They have drawn these exercises from their own work, from the work of their associated research groups as well as from published work.
After an eclipse of some 50 years, Number Theory, that is to say the study of the properties of the integers, has regained in France a vitality worthy of its distinguished past. More 'and more researchers have been attracted by problems which, though it is possible to express in simple statements, whose solutions require all their ingenuity and talent. In so doing, their work enriches the whole of mathematics with new and fertile methods. To be in a position to tackle these problems, it is neces sary to be familiar with many specific aspects of number theory. These are very different from those encountered in analysis or geometry. The necessary know-how can only be acquired by study ing and solving numerous problems. Now it is very easy to form ulate problems whose solutions, while sometimes obvious, more often go beyond current methods. Moreover, there is no doubt that, even more than in other disciplines, in mathematics one must have exercises available whose solutions are accessible. This is the objective realised by this work. It is the collab orative work of several successful young number theorists. They have drawn these exercises from their own work, from the work of their associated research groups as well as from published work.
1: Prime Numbers: Arithmetic Functions: Selberg’s Sieve.- 2: Additive Theory.- 3: Rational Series.- 4: Algebraic Theory.- 5: Distribution Modulo 1.- 6: Transcendental Numbers.- 7: Congruences Modp: Modular Forms.- 8: Quadratic Forms.- 9: Continued Fractions.- 10: p-ADIC Analysis.- Index of Terminology.- Index of Symbols and Notations.
| Erscheint lt. Verlag | 3.12.2010 |
|---|---|
| Reihe/Serie | Problem Books in Mathematics |
| Zusatzinfo | X, 542 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 1690 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| ISBN-10 | 1-4419-3071-X / 144193071X |
| ISBN-13 | 978-1-4419-3071-2 / 9781441930712 |
| Zustand | Neuware |
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