16:00 – 17:00pm
Online, Zoom Webinar
We’re very excited to welcome Kaisa Matomäki (University of Turku, Finland), as a Heilbronn Virtual Visiting Professor. For further information and to register for the colloquium, please visit the event website.
Title: On primes and other interesting sequences in short intervals
Abstract: By the prime number theorem, the number of primes up to $x$ is known to be asymptotically $x/\log x$. This suggests that whenever $H \leq x$ is reasonably large, the interval $[x, x+H]$ contains about $H/\log x$ primes. I will discuss what is known and what is not known about primes and almost primes (i.e. numbers with only few prime factors) in short intervals.
I will also talk about the Riemann zeta function and the Liouville function (defined, for an integer $n$, to be $+1$ or $-1$ depending on whether $n$ has an even or odd number of prime factors), both of which are closely connected to the prime numbers.
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