Math 139 041825 Dirichlet's Theorem on Arithmetic Progressions Part 1 скачать в хорошем качестве

Math 139 041825 Dirichlet's Theorem on Arithmetic Progressions Part 1

Statement of Dirichlet's theorem. First goal: to prove Euler's product formula for the zeta function. Crash course on infinite products: definition of convergence; condition ensuring convergence. Definition of zeta function. Comment on convergence. Idea of Euler's product formula. Rigorous proof of. Theorem: Euler's analytic version of the infinitude of primes. Lemma on ln(1+x). Lemma relating the sum of prime reciprocals and the logarithm of the zeta function. Proof of the infinitude of primes. Terminology. Euler phi-function. Characteristic function of ell. Extension to the integers. Dirichlet character mod q (extension of a character to the integers).