A multidimensional version of a result of Davenport-Erdos

O. Yeat Chan, Geumlan Choi, Alexandra Zaharescu

Research output: Contribution to journalArticlepeer-review


Davenport and Erdos showed that the distribution of values of sums of the form Sh(x) = ∑m=x+1x+h (m/p), where p is a prime and (m/p) is the Legendre symbol, is normal as h,p → ∞ such that log h/log p → 0. We prove a similar result for sums of the form S h(x1,..., xn) = ∑z1=x1+1 x1+h ⋯ ∑zn=xn+1xn+h (z1 +...+zn/p).

Original languageEnglish (US)
JournalJournal of Integer Sequences
Issue number2
StatePublished - 2003


  • Legendre symbol
  • Normal distribution

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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