engleski

Delsarte's Method in Number Theory

Delsarte's method consists of finding appropriate "witness" functions in a chosen compact Abelian topological group, such that its Fourier transform is non-negative, and so bounding cardinality of certain sets. We discuss applications of the method to difference sets of integers, uniform distribution properties of certain sets of integers, but also some other problems in number theory and ergodic theory. Specifically, we apply it to obtain bounds on sets whose difference set does not contain shifted primes $p-1$, and also new bounds related to the van der Corput property of integer polynomials.

Delsarte's method; Fourier transform; difference sets; van der Corput sets; primes

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