Description
There are several results of analytic number theory which
require information about the prime values of a multiplicative
function and return information about its averages. A characteristic
example of such a result is the Landau-Selberg-Delange method. In this
talk, we are interested in the opposite direction. In particular, we
are going to see that if $f$ is a suitable divisor-bounded
multiplicative function with rather small partial sums, then
$f(p)\approx -p^{i\gamma_1}-\cdots -p^{i\gamma_m}$ on average, where
the $\gamma_j$'s are the ordinates of the zeroes of the Dirichet
series of $f$ on the line $\Re(s)=1$. This extends a result of
Koukoulopoulos and Soundararajan from 2020 by building on ideas
coming from the work of Koukoulopoulos on the specific case
$|f|\leqslant 1$.
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Zoom link: https://us06web.zoom.us/j/81054493030?pwd=YoRbvi6py7Qb0ADjxIZoEVQBIcEMge.1
Meeting ID: 810 5449 3030
Passcode: 873115