**Graduate Studies in Mathematics**

Volume: 190;
2018;
240 pp;
Hardcover

MSC: Primary 11;

Print ISBN: 978-1-4704-4289-7

Product Code: GSM/190

List Price: $83.00

AMS Member Price: $66.40

MAA Member Price: $74.70

**Electronic ISBN: 978-1-4704-4727-4
Product Code: GSM/190.E**

List Price: $83.00

AMS Member Price: $66.40

MAA Member Price: $74.70

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#### Supplemental Materials

# Lectures on Finite Fields

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*Xiang-dong Hou*

The theory of finite fields encompasses algebra, combinatorics, and number theory and has furnished widespread applications in other areas of mathematics and computer science. This book is a collection of selected topics in the theory of finite fields and related areas. The topics include basic facts about finite fields, polynomials over finite fields, Gauss sums, algebraic number theory and cyclotomic fields, zeros of polynomials over finite fields, and classical groups over finite fields. The book is mostly self-contained, and the material covered is accessible to readers with the knowledge of graduate algebra; the only exception is a section on function fields. Each chapter is supplied with a set of exercises. The book can be adopted as a text for a second year graduate course or used as a reference by researchers.

#### Readership

Graduate students and researchers interested in number theory, in particular, the theory of finite fields.

#### Table of Contents

# Table of Contents

## Lectures on Finite Fields

- Cover Cover11
- Title page i2
- Contents v6
- Preface vii8
- Chapter 1. Preliminaries 112
- Chapter 2. Polynomials over Finite Fields 2334
- Chapter 3. Gauss Sums 5768
- Chapter 4. Algebraic Number Theory 7788
- Chapter 5. Zeros of Polynomials over Finite Fields 111122
- Chapter 6. Classical Groups 143154
- 6.1. The General Linear Group and Its Related Groups 144155
- 6.2. Simplicity of 𝑃𝑆𝐿(𝑛,𝐹) 146157
- 6.3. Conjugacy Classes of 𝐺𝐿(𝑛,𝔽_{𝕢}) 153164
- 6.4. Conjugacy Classes of 𝐴𝐺𝐿(𝑛,𝔽_{𝕢}) 160171
- 6.5. Bilinear Forms, Hermitian Forms, and Quadratic Forms 172183
- 6.6. Groups of Spaces Equipped with Forms 192203
- Exercises 215226

- Bibliography 221232
- List of Notation 223234
- Index 227238
- Back Cover Back Cover1242