Orthogonality of restricted primes with nilsequences
Christopher Frei (TU Graz)
Wednesday 12th June 16:00-17:00 Maths 110
Abstract
The randomness of arithmetic functions with respect to linear
correlations can be measured by Gowers uniformity norms. We show that
the von Mangoldt function of primes restricted to a fixed Chebotarev
class varies randomly around its average, up to structure arising from
congruences to small moduli. By the inverse theory of Green-Tao-Ziegler,
we can achieve this by studying correlations with nilsequences. Under
GRH, we get analogous results for primes with a prescribed primitive root.
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