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 language | English |
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Pages (from-to) | 195-215 |
Number of pages | 21 |
Journal | Finite Fields and Their Applications |
Volume | 39 |
DOIs | |
State | Published - 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