13 citations · 45 across the 29 of their papers we have counts for
4 papers · 1 filter
Three conjectures about character sums
Andrew Granville, Alexander P. Mangerel
We establish that three well-known and rather different looking conjectures about Dirichlet characters and their (weighted) sums, (concerning the Pólya-Vinogradov theorem for maxim…
Squarefrees are Gaussian in short intervals
Ofir Gorodetsky, Alexander P. Mangerel, Brad Rodgers
We show that counts of squarefree integers up to in short intervals of size tend to a Gaussian distribution as long as and . This answers…
Additive functions in short intervals, gaps and a conjecture of Erdős
Alexander P. Mangerel
With the aim of treating the local behaviour of additive functions, we develop analogues of the Matomäki-Radziwill theorem that allow us to approximate the average of a general add…
Divisor-bounded multiplicative functions in short intervals
Alexander P. Mangerel
We extend the Matomäki-Radziwiłł theorem to a large collection of unbounded multiplicative functions that are uniformly bounded, but not necessarily bounded by 1, on the primes. Ou…