التفاصيل البيبلوغرافية
| العنوان: |
A note on the density of k-free polynomial sets, Haar measure and global fields. |
| المؤلفون: |
Demangos, Luca1 Luca.Demangos@xjtlu.edu.cn, Longhi, Ignazio2 ignaziol@iisc.ac.in |
| المصدر: |
QM - Quaestiones Mathematicae. Oct2022, Vol. 45 Issue 9, p1373-1397. 25p. |
| مصطلحات موضوعية: |
*HAAR integral, *RINGS of integers, *POLYNOMIALS, *DENSITY, *MEASURE theory |
| مستخلص: |
In this work we investigate the general relation between the density of a subset of the ring of integers D of a general global field and the Haar measure of its closure in the profinite completion. We then study a specific family of sets, the preimages of k-free elements (for any given k ∈ ℕ\{0, 1}) via one variable polynomial maps, showing that under some hypotheses their asymptotic density always exists and it is precisely the Haar measure of the closure in of their set. [ABSTRACT FROM AUTHOR] |
| قاعدة البيانات: |
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