User:Vipul

I'm Vipul, the person who came up with the original idea for this website.

Notes for stuff I plan to expand

Euler totient function

In Euler totient function, to Measures of difference, add entries for $\ln (\phi (n)/n)/\ln n$, $\ln (\phi (n)/n)/\ln \ln n$, $\ln (\phi (n)/n)/\ln \ln \ln n$ for various $D$. I expect 0 at primes for all, and 0, 0, -1 at primorials since $(1-1/p)$ for a primorial should have log approx $-\ln \ln \ln n$.

Multiplicative and completely multiplicative functions

• Multiplicative functions form abelian group under Dirichlet product: Characterize the group as an external direct product of countably many (prime-indexed) copies of $1+xR[[x]]$ under multiplication (a formal group law on the power series)
• Multiplicative function: Mention the above characterization
• Modified Dirichlet character: Make a page on these
• Completely multiplicative function
  • Mention modified Dirichlet characters
  • Discuss their generating role in all the "interesting" parts of the group of multiplicative functions (basically, everything that shows up in our study is a finite Euler product, or a convolution of finitely many completely multiplicative functions and their inverses)