2009 Number Theory Seminar - 07
Topic
Moments of the error term in the Dirichlet divisor problem
Speakers
Details
In 1849, Dirichlet showed that sum_{n le x} d(n) = x(log
x+2gamma-1)+Delta(x) with Delta(x) ll sqrt{x} where d(n) counts the
number of divisors of n and gamma is the Euler constant. An interesting
problem is to study the behaviour of Delta(x), for instance, its true
order of magnitude and oscillations. We shall explore the various
moments of this error term.
