For an irrational real number and real number we consider the inhomogeneous approximation constant via the semi-regular negative continued fraction expansion of and an appropriate alpha-expansion of . We give an upper bound on the case of worst inhomogeneous approximation, which is sharp when the partial quotients ai are almost all even and at least four. When the negative expansion has period one we give a complete description of the spectrum of values above the first limit point.
Pour un nombre irrationnel et un nombre réel , on considère la constante d’approximation non-homogène en rapport avec le développement en fraction continue négatif semi-régulier de et un -développement adéquat de . Nous donnons une majoration de dans le cas où est mal approximé, qui s’avère fine lorsque les quotients partiels sont presque tous pairs et supérieurs ou égaux à . Lorsque le développement de est de période , on décrit entièrement le spectre des valeurs prises par au-dessus du premier point d’accumulation.
@article{JTNB_2001__13_2_539_0, author = {Christopher G. Pinner}, title = {More on inhomogeneous diophantine approximation}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {539--557}, publisher = {Universit\'e Bordeaux I}, volume = {13}, number = {2}, year = {2001}, doi = {10.5802/jtnb.337}, zbl = {1014.11043}, mrnumber = {1879672}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.337/} }
TY - JOUR TI - More on inhomogeneous diophantine approximation JO - Journal de Théorie des Nombres de Bordeaux PY - 2001 DA - 2001/// SP - 539 EP - 557 VL - 13 IS - 2 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.337/ UR - https://zbmath.org/?q=an%3A1014.11043 UR - https://www.ams.org/mathscinet-getitem?mr=1879672 UR - https://doi.org/10.5802/jtnb.337 DO - 10.5802/jtnb.337 LA - en ID - JTNB_2001__13_2_539_0 ER -
Christopher G. Pinner. More on inhomogeneous diophantine approximation. Journal de Théorie des Nombres de Bordeaux, Volume 13 (2001) no. 2, pp. 539-557. doi : 10.5802/jtnb.337. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.337/
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