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Number Theory Lectures

This note covers the following topics: Divisibility and Primes, Congruences, Congruences with a Prime-Power Modulus, Euler's Function and RSA Cryptosystem, Units Modulo an Integer, Quadratic Residues and Quadratic Forms, Sum of Powers, Fractions and Pell's Equation, Arithmetic Functions, The Riemann Zeta Function and Dirichlet L-Function.

Author(s): Dr. Anupam Saikia, NTPEL

NA Pages

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Number Theory by Lars Ake Lindahl

This PDF covers the following topics related to Number Theory : Divisibility, Prime Numbers, The Linear Diophantine Equation , Congruences, Linear Congruences, The Chinese Remainder Theorem, Public-Key Cryptography, Pseudoprimes, Polynomial Congruences with Prime Moduli, Polynomial Congruences with Prime Power Moduli, The Congruence, General Quadratic Congruences, The Legendre Symbol and Gauss� Lemma, Quadratic Reciprocity, Primitive Roots, Arithmetic Functions, Sums of Squares, Pythagorean Triples, Fermat�s Last Theorem, Continued Fractions, Simple Continued Fractions, Rational Approximations to Irrational Numbers, Periodic Continued Fractions, Continued Fraction Expansion, Pell�s Equation.

Author(s): Lars Ake Lindahl

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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

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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

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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 Lectures

Number Theory Lectures

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