An uncertainty principle for cyclic groups of prime order

Abstract

Let G be a finite abelian group, and let f : G → C be a complex function on G.The uncertainty principle asserts that the support supp(fwhere |X| denotes the cardinality of X.In this note we show that when G is the cyclic group Z/pZ of prime order p, then we may improve this toand show that this is absolutely sharp.As one consequence, we see that a sparse polynomial in Z/pZ consisting of k + 1 monomials can have at most k zeroes.Another consequence is a short proof of the well-known Cauchy-Davenport inequality.

Locations

• Mathematical Research Letters - View - PDF
• arXiv (Cornell University) - View
• Mathematical Research Letters - View - PDF
• arXiv (Cornell University) - View