Effective equidistribution of lattice points in positive characteristic
Horesh T, Paulin F. 2022. Effective equidistribution of lattice points in positive characteristic. Journal de Theorie des Nombres de Bordeaux. 34(3), 679–703.
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Author
Horesh, TalISTA;
Paulin, Frédéric
Corresponding author has ISTA affiliation
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Abstract
Given a place ω of a global function field K over a finite field, with associated affine function ring Rω and completion Kω , the aim of this paper is to give an effective joint equidistribution result for renormalized primitive lattice points (a,b)∈Rω2 in the plane Kω2 , and for renormalized solutions to the gcd equation ax+by=1 . The main tools are techniques of Goronik and Nevo for counting lattice points in well-rounded families of subsets. This gives a sharper analog in positive characteristic of a result of Nevo and the first author for the equidistribution of the primitive lattice points in \ZZ2 .
Publishing Year
Date Published
2022-01-27
Journal Title
Journal de Theorie des Nombres de Bordeaux
Publisher
Centre Mersenne
Acknowledgement
The authors warmly thank Amos Nevo for having presented the authors to each other during
a beautiful conference in Goa in February 2016, where the idea of this paper was born. The
first author thanks the IHES for two post-doctoral years when most of this paper was discussed,
and the Topology team in Orsay for financial support at the final stage. The first author was
supported by the EPRSC EP/P026710/1 grant. Finally, we warmly thank the referee for many
very helpful comments that have improved the readability of this paper.
Volume
34
Issue
3
Page
679-703
ISSN
eISSN
IST-REx-ID
Cite this
Horesh T, Paulin F. Effective equidistribution of lattice points in positive characteristic. Journal de Theorie des Nombres de Bordeaux. 2022;34(3):679-703. doi:10.5802/JTNB.1222
Horesh, T., & Paulin, F. (2022). Effective equidistribution of lattice points in positive characteristic. Journal de Theorie Des Nombres de Bordeaux. Centre Mersenne. https://doi.org/10.5802/JTNB.1222
Horesh, Tal, and Frédéric Paulin. “Effective Equidistribution of Lattice Points in Positive Characteristic.” Journal de Theorie Des Nombres de Bordeaux. Centre Mersenne, 2022. https://doi.org/10.5802/JTNB.1222.
T. Horesh and F. Paulin, “Effective equidistribution of lattice points in positive characteristic,” Journal de Theorie des Nombres de Bordeaux, vol. 34, no. 3. Centre Mersenne, pp. 679–703, 2022.
Horesh T, Paulin F. 2022. Effective equidistribution of lattice points in positive characteristic. Journal de Theorie des Nombres de Bordeaux. 34(3), 679–703.
Horesh, Tal, and Frédéric Paulin. “Effective Equidistribution of Lattice Points in Positive Characteristic.” Journal de Theorie Des Nombres de Bordeaux, vol. 34, no. 3, Centre Mersenne, 2022, pp. 679–703, doi:10.5802/JTNB.1222.
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