Table of Contents

I—Algebraic Methods.- I—Finite fields.- II — p-adic fields.- III—Hilbert symbol.- IV—Quadratic forms over Qp and over Q.- V—Integral quadratic forms with discriminant ± 1.- II—Analytic Methods.- VI—The theorem on arithmetic progressions.- VII—Modular forms.- Index of Definitions.- Index of Notations.

Reviews

“The book is a showcase of how some results in classical number theory (the Arithmetic of the title) can be derived quickly using abstract algebra. … There are a reasonable number of worked examples, and they are very well-chosen. … this book will expand your horizons, but you should already have a good knowledge of algebra and of classical number theory before you begin.” (Allen Stenger, MAA Reviews, maa.org, July, 2016)