Tuesday 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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