Linear patterns of prime elements in number fields

Abstract: I will discuss my recent result that gives a sufficient condition for a set of finitely many polynomials of degree 1 with coefficients in a number ring to attain simultaneous prime values. This extends a 2012 theorem of Green-Tao-Ziegler from the case of Z to the general case. Time permitting, I will mention how this can be applied to produce (modestly) new families of varieties over number fields which satisfy the Hasse principle for rational points by using the so-called fibration methods.

number theory

Audience: researchers in the topic

London number theory seminar

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For a record of talks predating this website see: wwwf.imperial.ac.uk/~buzzard/LNTS/numbtheo_past.html