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 necesยญ 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 studyยญ ing and solving numerous problems. Now it is very easy to formยญ 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 collabยญ 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
CONTENT
1: Prime Numbers: Arithmetic Functions: Selbergโs 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
