You are cordially invited to the Number Theory Seminar organized by the Department of Mathematics.
Speaker: Tomos Parry (Bilkent)
” Selberg’s sieve”
Abstract: A sieve picks out the numbers left over after removing multiples of certain primes, using an indicator function like
∑_(d|n)▒〖μ(d)〗={█(1 for n=1@0 for & n>1.)┤
If we are prepared to accept upper bounds instead of equality, then Selberg’s observation is that we can replace the above with
(∑_(d|n)▒γ(d) )^2≥{█(1 for n=1@0 for n=0)┤
where γ(d) is any value we want as long as γ(1)=1.
The simplicity of this a square is positive" bound therefore gives us a lot of freedom in choosing γ(d). This gives results as strong as the earlier (combinatorial”) sieves.
Date: Friday, May 30, 2025
Time: 19:00
Place: SB-Z11