Quadratic residues and non-residues : selected topics /
This book offers an account of the classical theory of quadratic residues and non-residues with the goal of using that theory as a lens through which to view the development of some of the fundamental methods employed in modern elementary, algebraic, and analytic number theory. The first three chapt...
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
[Cham] Switzerland :
Springer,
[2016]
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| Series: | Lecture notes in mathematics (Springer-Verlag)
2171. |
| Subjects: |
Table of Contents:
- Introduction: Solving the General Quadratic Congruence Modulo a Prime
- Basic Facts
- Gauss' Theorema Aureum: the Law of Quadratic Reciprocity
- Four Interesting Applications of Quadratic Reciprocity
- The Zeta Function of an Algebraic Number Field and Some Applications
- Elementary Proofs
- Dirichlet L-functions and the Distribution of Quadratic Residues
- Dirichlet's Class-Number Formula
- Quadratic Residues and Non-residues in Arithmetic Progression
- Are quadratic residues randomly distributed?
- Bibliography.