Pair correlation of squares in p-adic fields

Research output: Contribution to journalArticle

Abstract

Let p be an odd prime number, K a p-adic field of degree r over Qp, O the ring of integers in K, B = {β1,..., βr} an integral basis of K over Qp, u a unit in O and consider sets of the form N = {n1β1 + ⋯ + nrβr : 1 ≤ nj ≤ Nj, 1 ≤ j ≤ r}. We show under certain growth conditions that the pair correlation of {uz2 : z ∈ N} becomes Poissonian.

Original languageEnglish (US)
Pages (from-to)432-448
Number of pages17
JournalCanadian Journal of Mathematics
Volume55
Issue number2
DOIs
StatePublished - Apr 2003

ASJC Scopus subject areas

  • Mathematics(all)

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