Date of Award
2019
Document Type
Thesis
Degree Name
M.S. in Mathematics
Department
Mathematics
First Advisor
Thai Hoang Le
Second Advisor
Erwin Mina Diaz
Third Advisor
Rizwanur Khan
Relational Format
dissertation/thesis
Abstract
The law of quadratic reciprocity is an important result in number theory. The purpose of this thesis is to present several proofs as well as applications of the law of quadratic reciprocity. I will present three proofs of the quadratic reciprocity. We begin with a proof that depends on Gauss's lemma and Eisenstein's lemma. We then describe another proof due to Eisentein using the $n$th roots of unity. Then we provide a modern proof published in 1991 by Rousseau. In the second part of the thesis, we present two applications of quadratic reciprocity. These include special cases of Dirichlet's theorem on primes in arithmetic progressions and Fermat's theorem on sums of two squares.
Recommended Citation
Almuteri, Awatef Noweafa, "Quadratic Reciprocity: Proofs and Applications" (2019). Electronic Theses and Dissertations. 1540.
https://egrove.olemiss.edu/etd/1540