Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imper- spicuous system of arguments which have tended to jump around all over the place.
7 Les Houches Number theory, or arithmetic, sometimes referred to as the queen of mathematics, is often considered as the purest branch of mathematics.
Owing to the developments and applications of computer science, ma- thematicians began to take a serious interest in the applications of number theory to numerical analysis about twenty years ago.
The problem of uniform distribution of sequences initiated by Hardy, Little- wood and Weyl in the 1910's has now become an important part of number theory.
The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great- est common divisor at least three centuries B.
Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.
The plan of this book had its inception in a course of lectures on arithmetical functions given by me in the summer of 1964 at the Forschungsinstitut fUr Mathematik of the Swiss Federal Institute of Technology, Zurich, at the invitation of Professor Beno Eckmann.
The main topic of the volume is to develop efficient algorithms by which one can verify Artin's conjecture for odd two-dimensional representations in a fairly wide range.
These notes are concerned with showing the relation between L-functions of classical groups (*F1 in particular) and *F2 functions arising from the oscillator representation of the dual reductive pair *F1 *F3 O(Q).
The relations that could or should exist between algebraic cycles, algebraic K-theory, and the cohomology of - possibly singular - varieties, are the topic of investigation of this book.
