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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
Theory of Numbers Lecture Notes
This lecture note is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.
Author(s): Prof. Abhinav Kumar
NA 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
