Read more
Zusatztext ...easily readable...The book can be warmly recommended not only to those with a preference for number theory but even for the general readership in pure mathematics or supervisors looking for creative examples for further motivation of scientific computations. Klappentext This graduate text! based on years of teaching experience! is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used as a tool for research in number theory through numerical experimentation. The book contains many examples of experiments in binary quadratic forms! zeta functions of varieties over finite fields! elementary class field theory! elliptic units! modular forms! along with exercises and selected solutions. Sample programs are written in GP! the scripting language for the computational package PARI! and are available for download from the author's website. Zusammenfassung This graduate text, based on years of teaching experience, is intended for first or second year graduate students in pure mathematics. The main goal of the text is to show how the computer can be used as a tool for research in number theory through numerical experimentation. The book contains many examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, along with exercises and selected solutions. Sample programs are written in GP, the scripting language for the computational package PARI, and are available for download from the author's website. Inhaltsverzeichnis Preface 1: Basic examples 2: Reciprocity 3: Positive definite binary quadratic forms 4: Sequences 5: Combinatorics 6: p-adic numbers 7: Polynomials 8: Remarks on selected exercises References Index
