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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 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
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
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
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
A Course on Number Theory (PDF 139P)
This note explains the following topics: Algebraic numbers, Finite continued fractions, Infinite continued fractions, Periodic continued fractions, Lagrange and Pell, Euler’s totient function, Quadratic residues and non-residues, Sums of squares and Quadratic forms.
Author(s): Peter J. Cameron
139 Pages
Lectures on Topics in Algebraic Number Theory (PDF 83P)
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NA Pages
A Modern Course on Curves and Surfaces
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A Course In Algebraic Number Theory
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Number theory and elementary arithmetic
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Number Theory and Cryptography
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An Introduction to p adic Numbers and p adic Analysis (PDF 64p)
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