Attività del Dipartimento

Colloquium di Matematica

In its simplest formulation, Artin’s 1927 conjecture on primitive roots
is a reasonable guess that can be discovered by anyone playing
with rational numbers on a hand calculator. We will do so in this talk,
before going into the more precise quantitative statements that 
Artin proposed, and much later had to correct in view of the numerical data
that were obtained when computers became available in the 1950s.
 Artin’s conjecture is still open, but it can be “proved" under assumption of the
generalised Riemann hypothesis; some generalisations remain unproved 
even under such assumptions, and some weaker statements
can be proved unconditionally. We will discuss a few of them,
and ultimately focus on the challenges we are facing in the setting 
of elliptic curves.
 
 
org: PAPPALARDI Francesco