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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, Chebyshev�s theorem.

Author(s): Vahagn Aslanyan

69 Pages

Analytic number theory provides some powerful tools to study prime numbers, and most of our current knowledge of primes has been obtained using these tools. Topics covered includes: Primes and the Fundamental Theorem of Arithmetic, Arithmetic functions: Elementary theory, Dirichlet series and Euler products and Asymptotic estimates, Distribution of primes: Elementary results and Proof of the Prime Number Theorem, Primes in arithmetic progressions.

Author(s): A.J. Hildebrand

NA 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

Algebraic Number Theory by Paul Garrett

This note contains the following subtopics: Classfield theory, homological formulation, harmonic polynomial multiples of Gaussians, Fourier transform, Fourier inversion on archimedean and p-adic completions, commutative algebra: integral extensions and algebraic integers, factorization of some Dedekind zeta functions into Dirichlet L-functions, meromorphic continuation and functional equation of zeta, Poisson summation and functional equation of theta, integral representation of zeta in terms of theta.

Author(s): Paul Garrett

NA Pages

The Theory of Numbers

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

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Number Theory Lecture Notes by Vahagn Aslanyan

Number Theory Lecture Notes by Vahagn Aslanyan

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