Author
Gorodetsky, O
Journal title
Mathematika
DOI
10.1112/s0025579317000092
Issue
2
Volume
63
Last updated
2024-03-24T21:51:22.32+00:00
Page
622-665
Abstract
Recently, an analogue over Fq[T] of Landau’s theorem on sums of two squares was considered by Bary-Soroker, Smilansky and Wolf. They counted the number of monic polynomials in Fq[T] of degree n of the form A2 + T B2, which we denote by B(n, q). They studied B(n, q) in two limits: fixed n and large q; and fixed q and large n. We generalize their result to the most general limit qn → ∞. More precisely, we prove
B(n, q) ∼ Kq ·n −12n!· qn, qn → ∞,
for an explicit constant Kq = 1 + O (1/q). Our methods are different and are based on giving explicit bounds on the coefficients of generating functions. These methods also apply to other problems, related to polynomials with prime factors of even degree.
Symplectic ID
1145835
Favourite
Off
Publication type
Journal Article
Publication date
05 Jun 2017
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