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Hooley's theorem and its avatars

Posted in
Pieter Moree
Wed, 2017-08-30 14:15 - 15:15
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

It is 50 years ago that C. Hooley proved the Artin primitive root conjecture assuming the Generalized
Riemann Hypothesis. It gives the density of primes p such that a given fixed basis number g has p as
a primitive root. Hooley's result shows that Artin's conjectural density has to be sometimes multiplied
by a somewhat mysterious correction factor. Soon Hooley's achievement will be honored in his presence
in a Heilbronn symposium in Bristol. My talk is a try-out for this event focusing on the prehistory, the theorem
itself and some later developments including the Lenstra-Moree-Stevenhagen character sum method that
allows one to understand the correction factor better and compute it much more directly for many variants
of the original problem.

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