On the function field analogue of Landau's theorem on sums of squares

Lior Bary-Soroker, Yotam Smilansky, Adva Wolf

Research output: Contribution to journalArticlepeer-review

Abstract

This paper deals with function field analogues of the famous theorem of Landau which gives the asymptotic density of sums of two squares in Z. We define the analogue of a sum of two squares in Fq[T], q odd and estimate the number Bq(n) of such polynomials of degree n in two cases. The first case is when q is large and n fixed and the second case is when n is large and q is fixed. Although the methods used and main terms computed in each of the two cases differ, the two iterated limits of (a normalization of) Bq(n) turn out to be exactly the same.

Original languageEnglish
Pages (from-to)195-215
Number of pages21
JournalFinite Fields and Their Applications
Volume39
DOIs
StatePublished - 1 May 2016

Keywords

  • Polynomials over finite fields
  • Sums of two squares

All Science Journal Classification (ASJC) codes

  • General Engineering
  • Theoretical Computer Science
  • Applied Mathematics
  • Algebra and Number Theory

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