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Zusatztext An extremely demanding text for undergraduates! but well-suited for a mathematician who wants to learn some number theory. Klappentext This textbook covers the main topics in number theory as taught in universities throughout the world. Number theory deals mainly with properties of integers and rational numbers; it is not an organized theory in the usual sense but a vast collection of individual topics and results, with some coherent sub-theories and a long list of unsolved problems. This book excludes topics relying heavily on complex analysis and advanced algebraic number theory. The increased use of computers in number theory is reflected in many sections (with much greater emphasis in this edition). Some results of a more advanced nature are also given, including the Gelfond-Schneider theorem, the prime number theorem, and the Mordell-Weil theorem. The latest work on Fermat's last theorem is also briefly discussed. Each chapter ends with a collection of problems; hints or sketch solutions are given at the end of the book, together with various useful tables. Zusammenfassung A new edition of this classic textbook, this book is the only publication which covers all the main areas of number theory, including up-to-date as well as established material. The increased use of computers in mathematics is reflected in the text, and each chapter ends with a collection of problems, with hints or sketch solutions provided at the end of the book together with useful tables. Inhaltsverzeichnis 1.: Divisibility 2.: Multiplicative Functions 3.: Congruence Theory 4.: Quadratic Residues 5.: Algebraic Topics 6.: Sums of Squares and Gauss Sums 7.: Continued Fractions 8.: Transcendental Numbers 9.: Quadratic Forms 10.: Genera and the Class Group 11.: Partitions 12.: The Prime Numbers 13.: Two Major Theorems on the Primes 14.: Diophantine Equations 15.: Elliptic Curves: Basic Theory 16.: Elliptic Curves: Further Results and Applications Answers and Hints to Problems Tables Bibliography Index to Notation General Index ...
