Abstract
We consider a Kurzweil type inhomogeneous Diophantine approximation theorem in the field of the formal Laurent series for a monotone sequence of approximation. We find a necessary and sufficient condition for irrational f and monotone increasing (ℓn) that there are infinitely many polynomials P and Q such that |Qf-P-g|<q-n-ℓn, n=deg(Q) for almost every g. We also study some conditions for irrational f such that for all monotone increasing (ℓn) with Σq- ℓn=∞ there are infinitely many solutions for almost every g.
Original language | English |
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Pages (from-to) | 64-75 |
Number of pages | 12 |
Journal | Finite Fields and their Applications |
Volume | 20 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2013 |
Keywords
- Formal Laurent series
- Inhomogeneous Diophantine approximation
- Kurzweil type theorem