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Prime and squarefree values of polynomials in moderately many variables

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Kevin Destagnol
Wed, 2018-01-17 16:30 - 17:30
MPIM Lecture Hall

We will present a generalisation of Schinzel's hypothesis and of the Bateman-Horn's conjecture concerning
prime values of a system of polynomials in one variable to the case of a integer form in many variables.
In particular, we will establish in this talk that a polynomial in moderately many variables takes infinitely
many prime (but also squarefree) values under some necessary assumptions. The proof will rely on Birch's
circle method and will be achieved in 50% fewer variables than in the classical Birch setting. Moreover it
can be applied to study the Hasse principle and weak approximation for some normic equations.

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