Text
On Generalized Thue-Morse Functions and Their Values
In this paper we extend and generalize, up to a natural bound of the method, our previous work Badziahin and Zorin [‘Thue–Morse constant is not badly approximable’, Int. Math. Res. Not. IMRN 19 (2015), 9618–9637] where we proved, among other things, that the Thue–Morse constant is not badly approximable. Here we consider Laurent series defined with infinite products fd(x)=∏∞n=0(1−x−dn), d∈N, d≥2, which generalize the generating function f2(x) of the Thue–Morse number, and study their continued fraction expansion. In particular, we show that the convergents of x−d+1fd(x) have a regular structure. We also address the question of whether the corresponding Mahler numbers fd(a)∈R, a,d∈N, a,d≥2, are badly approximable.
Barcode | Tipe Koleksi | Nomor Panggil | Lokasi | Status | |
---|---|---|---|---|---|
art137276 | null | Artikel | Gdg9-Lt3 | Tersedia namun tidak untuk dipinjamkan - No Loan |
Tidak tersedia versi lain