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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
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
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
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
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
A Modern Course on Curves and Surfaces
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Author(s): NA
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A Computational Introduction to Number Theory
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A Course In Algebraic Number Theory
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Combinatorial and Analytic Number Theory
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Elementary Number Theory Clark W.E.
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An Introduction to the Theory of Numbers
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NA Pages
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An Introduction to p adic Numbers and p adic Analysis (PDF 64p)
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NA Pages
Algebra and Number Theory (PDF 64p)
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