Multiplicative Functions and Dirichlet Series via Boxes - Math Foundations 242

Explore the rich mathematical landscape of multiplicative functions and their connection to Dirichlet series in this 26-minute video lecture. Delve into the Fundamental Identity of Arithmetic as a source of interesting number theoretic identities. Learn how to apply multiplicative functions from natural numbers to natural numbers or integers to this fundamental identity. Examine sums of divisors, related functions, and Euler's totient function through explicit computations, revealing non-trivial and unexpected identities. Discover how this development naturally connects to the theory of Dirichlet series in analytic number theory. Gain insights into a broader landscape of mathematical identities that can be investigated using similar techniques.