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A polynomial analogue of Landau's theorem and related problems

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 me...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/s0025579317000092

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Wiley
Journal:
Mathematika More from this journal
Volume:
63
Issue:
2
Pages:
622-665
Publication date:
2017-06-05
Acceptance date:
2017-03-10
DOI:
EISSN:
2041-7942
ISSN:
0025-5793
Language:
English
Keywords:
Pubs id:
1145835
Local pid:
pubs:1145835
Deposit date:
2020-11-16

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