Journal article
The variance of the number of sums of two squares in Fq[T] in short intervals
- Abstract:
- Consider the number of integers in a short interval that can be represented as a sum of two squares. What is an estimate for the variance of these counts over random short intervals? We resolve a function field variant of this problem in the large q limit, finding a connection to the z-measures first investigated in the context of harmonic analysis on the infinite symmetric group. A similar connection to z-measures is established for sums over short intervals of the divisor functions dz(n). We use these results to make conjectures in the setting of the integers which match very well with numerically produced data. Our proofs depend on equidistribution results of N. Katz and W. Sawin.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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Access Document
- Files:
-
-
(Preview, Accepted manuscript, pdf, 741.6KB, Terms of use)
-
- Publisher copy:
- 10.1353/ajm.2021.0044
Authors
- Publisher:
- Johns Hopkins University Press
- Journal:
- American Journal of Mathematics More from this journal
- Volume:
- 143
- Issue:
- 6
- Pages:
- 1703-1745
- Publication date:
- 2021-12-04
- DOI:
- EISSN:
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1080-6377
- ISSN:
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0002-9327
- Language:
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English
- Keywords:
- Pubs id:
-
1235966
- Local pid:
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pubs:1235966
- Deposit date:
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2024-02-13
Terms of use
- Copyright date:
- 2021
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Johns Hopkins University Press at: https://dx.doi.org/10.1353/ajm.2021.0044
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