von Mangoldt function
- Category
- RIEMANN HYPOTHESIS
- Definition
- The arithmetic function Lambda(n), equal to log p on prime powers p^k and zero otherwise.
- Math Level
- GENERAL
- Index Excerpt
- Lambda(n); Λ(n)
von Mangoldt function
The von Mangoldt function assigns when is a positive power of a prime , and assigns zero otherwise.
It packages primes and prime powers into a form that is especially natural in analytic number theory, Dirichlet series and explicit formulas.
See also: prime number, prime power, Riemann zeta function. .