## Heilbronn Colloquium 2021: Kaisa Matomäki

10 Feb 2021, by Events inTuesday 4 May 2021 at 16:00

Organised in collaboration with the School of Mathematics, University of Bristol, UK

**On Primes and Other Interesting Sequences in Short Intervals**

Kaisa Matomäki, University of Turku, Finland

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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