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Analytic Number Theory Lecture Notes by Andreas Strombergsson
This note covers the following topics: Primes in Arithmetic Progressions, Infinite products, Partial summation and Dirichlet series, Dirichlet characters, L(1, x) and class numbers, The distribution of the primes, The prime number theorem, The functional equation, The prime number theorem for Arithmetic Progressions, Siegel’s Theorem, The Polya-Vinogradov Inequality, Sums of three primes, The Large Sieve, Bombieri’s Theorem.
Author(s): Andreas Strombergsson
295 Pages 
A Computational Introduction to Number Theory and Algebra
This note contains below topics, Title, Preliminaries, Basic properties of the integers, Congruences, Computing with large integers, Euclid s algorithm, The distribution of primes, Abelian groups, Rings, Finite and discrete probability distributions, Probabilistic algorithms, Probabilistic primality testing, Finding generators and discrete logarithms in Zp, Quadratic reciprocity and computing modular square roots, Modules and vector spaces, Matrices, Subexponentialtime discrete logarithms and factoring, More rings.
Author(s): Victor Shoup
598 Pages
Modular Functions and Modular Forms
This book contains below topics, A First Course in Modular Forms, Springer GUNNING, Introduction to Elliptic Curves and Modular Forms, Elliptic Curves, Booksurge Available on my website MIYAKE, Cours dArithmetique, Presses Univ de France The last.
Author(s): J.S. Milne
134 Pages
Lectures notes on number theory for computer science
This brief collects notes on elementary and medium level number theory, mainly for computer science students. It can support a discrete mathematics course, a foundations course, or a cryptography course. The opening chapters cover divisibility, primes, modular arithmetic, and Eulers totient function.
Author(s): Alexandros V. Gerbessiotis
191 Pages
Number Theory Lecture Notes by Vahagn Aslanyan
This note explains the following topics, Divisibility, Multiplicative functions, Modular arithmetic, Primitive roots, Quadratic residues, Diophantine equations, Quadratic number fields, Chebyshevs theorem.
Author(s): Vahagn Aslanyan
69 Pages
Elementary Number Theory Primes Congruences and Secrets
This is a textbook about classical elementary number theory and elliptic curves. The first part discusses elementary topics such as primes, factorization, continued fractions, and quadratic forms, in the context of cryptography, computation, and deep open research problems. The second part is about elliptic curves, their applications to algorithmic problems, and their connections with problems in number theory.
Author(s): William Stein
NA Pages
Robert Daniel Carmichael March 1, 1879 May 2, 1967 was a leading American mathematician.The purpose of this little book is to give the reader a convenient introduction to the theory of numbers, one of the most extensive and most elegant disciplines in the whole body of mathematics. The arrangement of the material is as follows, The five chapters are devoted to the development of those elements which are essential to any study of the subject. The sixth and last chapter is intended to give the reader some indication of the direction of further study with a brief account of the nature of the material in each of the topics suggested.
Author(s): R. D. Carmichael
88 Pages