Journal article
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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Authors
Bibliographic Details
- Publisher:
- Wiley Publisher's website
- Journal:
- Mathematika Journal website
- Volume:
- 63
- Issue:
- 2
- Pages:
- 622-665
- Publication date:
- 2017-06-05
- Acceptance date:
- 2017-03-10
- DOI:
- EISSN:
-
2041-7942
- ISSN:
-
0025-5793
Item Description
- Language:
- English
- Keywords:
- Pubs id:
-
1145835
- Local pid:
- pubs:1145835
- Deposit date:
- 2020-11-16
Terms of use
- Copyright holder:
- University College London
- Copyright date:
- 2017
- Rights statement:
- © 2017 University College London.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Wiley at: https://doi.org/10.1112/S0025579317000092
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