[Liste-CICMA] QVNTS tomorrow

Dimitris Koukoulopoulos koukoulo at DMS.UMontreal.CA
Wed Dec 3 19:02:12 EST 2014

Dear all,

Here is the information for tomorrow's talks:

Title: Additive decompositions of some interesting sets Abstract: We say a
set is asymptotically additively decomposable if it can be written as a
sumset A+B apart from finitely many mistakes, for some sets A,B of at least
two positive integers. Most sets are not asymptotically additively
decomposable, so it is natural to conjecture that arithmetically
interesting sets like primes and smooth numbers are not. I will try to
describe some of the progress that has been made on these questions. (Based
on joint work with Christian Elsholtz.)

14:00-15:30: Florian Luca (University of the Witwatersrand)

Title: On the counting function of irregular primes Abstract: A prime $p>3$
is irregular if it divides the numerator of one of the Bernoulli numbers
$B_2,\ldots,B_{p-3}$. It is known that there are infinitely many irregular
primes. In my talk, I will show that the number of irregular primes $p\le x$ is at least as large as $(1+o(1))\log\log x/\log\log\log x$ as
$x\to\infty$. The proof uses sieves and linear forms in logarithms. This is
joint work with Amalia Pizarro from the University of Valparaiso, Chile and
Carl Pomerance from Dartmouth College.

Best wishes,
Dimitris
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