UCalgary Algebra and Number Theory Seminar: Nicol Leong

The summatory Mobius function M ( x ) is an important arithmetic function in number theory that contains information regarding primes and square-free numbers, and has strong links to the Riemann zeta function. Its growth rate is a difficult subject study due to the oscillatory nature of M ( x ) , but has nevertheless garnered much interest, since a strong enough bound on M ( x ) is equivalent to the Riemann hypothesis (RH). On the other hand, since we do not yet have RH, it is a good idea to see what are the strongest (explicit) bounds we can obtain unconditionally. This is part of a joint work with Ethan Lee. We will also discuss an application of these explicit M ( x ) estimates to study the behaviour and growth rates of other similar oscillatory arithmetic functions. This work is joint with Daniel Johnston and Sebastian Tudzi.