Pathway XXI

L(s)Arithmetic functions and L-series

Möbius inversion, Euler products, and the Riemann zeta function as a product over primes.

1. 01Zeta and Euler productsζ(s) = ∑ n⁻ˢ = ∏ (1 − p⁻ˢ)⁻¹. The product is the sieve written in analysis.4 min
2. 02Möbius inversionμ(n) is 0 on squares, (−1)^k on k distinct primes. It inverts Euler’s product.4 min