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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
95 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
Introduction to Analytic Number Theory Lecture Notes
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
An Introductory Course in Elementary Number Theory
The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. Proofs of basic theorems are presented in an interesting and comprehensive way that can be read and understood even by non-majors with the exception in the last three chapters where a background in analysis, measure theory and abstract algebra is required.
Author(s): Wissam Raji
171 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
Introductory Number Theory (PDF 80P)
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Automorphic Forms, Representations, and L Functions
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A Computational Introduction to Number Theory
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Number theory and elementary arithmetic
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Combinatorial and Analytic Number Theory
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Number Theory and Cryptography
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Elementary Number Theory Clark W.E.
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Algebra and Number Theory (PDF 64p)
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