Experimental Number Theory - Villegas, Fernando Rodriguez; - Prospero Internet Bookshop
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Experimental Number Theory
 
Product details:
ISBN13:9780198528227
ISBN10:0198528221
Binding:Hardback
No. of pages:232 pages
Size:240x160x16 mm
Weight:480 g
Language:English
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Category:

Experimental Number Theory

 
Publisher: OUP Oxford
Date of Publication:
 
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Short description:

This graduate text shows how the computer can be used as a tool for research in number theory through numerical experimentation. Examples of experiments in binary quadratic forms, zeta functions of varieties over finite fields, elementary class field theory, elliptic units, modular forms, are provided along with exercises and selected solutions.

Long description:
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.
Table of Contents:
Preface
Basic examples
Reciprocity
Positive definite binary quadratic forms
Sequences
Combinatorics
p-adic numbers
Polynomials
Remarks on selected exercises
References
Index