grandes-ecoles 2022 Q7.5

grandes-ecoles · France · x-ens-maths-d__mp Number Theory Arithmetic Functions and Multiplicative Number Theory

Let $p$ be a prime number and $\alpha\geq 1$ be an integer. Show that $$L_{\mathrm{prim}}(u,v,p^\alpha) = L(u,v,p^\alpha) - L(u,v,p^{\alpha-1}).$$

Let $p$ be a prime number and $\alpha\geq 1$ be an integer. Show that
$$L_{\mathrm{prim}}(u,v,p^\alpha) = L(u,v,p^\alpha) - L(u,v,p^{\alpha-1}).$$