[Liste-CICMA] Seminar Tomorrow

Farzad Aryan aryan at CRM.Umontreal.ca
Wed Aug 3 13:51:36 EDT 2016

Dear all,

Tomorrow at 11:00 am in room 5448 André Aisenstadt, Dimitris Koukoulopoulos
(University of Montreal) will give a talk.

Title: Sieve weights and their smoothings

Abstract: I will discuss moments of partially smoothed, truncated divisor
sums of the M\"obius function. Such divisor sums appear naturally in the
theory of the Selberg sieve and they play a key role in the GPY sieve and
its recent improvements due to Maynard and Tao. It turns out that if the
truncation is smooth enough, the main contribution to the moments comes
from almost primes. However, for rougher truncations, the dominant
contribution comes from integers with many prime factors.

Analogous questions can be asked for polynomials over finite fields and
for permutations, and in these cases the moments behave rather
differently, a rare exception. As we will see, a plausible explanation for
this phenomenon is given by studying the analogous sums for Dirichlet
characters and obtaining different answers depending on whether or not the
character is ``exceptional''.

This is joint work with Andrew Granville and James Maynard.

See you there,

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