Experimental number theory
著者
書誌事項
Experimental number theory
(Oxford graduate texts in mathematics, 13)
Oxford University Press, 2007
- : pbk
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注記
Bibliography: p. [205]-210
Includes index
内容説明・目次
内容説明
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.
目次
- 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
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