Diophantine approximation on rational quadrics
نویسندگان
چکیده
منابع مشابه
Diophantine approximation on rational quadrics
We compute the Hausdorff dimension of sets of very well approximable vectors on rational quadrics. We use ubiquitous systems and the geometry of locally symmetric spaces. As a byproduct we obtain the Hausdorff dimension of the set of rays with a fixed maximal singular direction, which move away into one end of a locally symmetric space at linear depth, infinitely many times.
متن کاملOn the Abc Conjecture and Diophantine Approximation by Rational Points
We show that an earlier conjecture of the author, on diophantine approximation of rational points on varieties, implies the “abc conjecture” of Masser and Oesterlé. In fact, a weak form of the former conjecture is sufficient, involving an extra hypothesis that the variety and divisor admit a faithful group action of a certain type. Analogues of this weaker conjecture are proved in the split fun...
متن کاملDiophantine Approximation on Veech
— We show that Y. Cheung’s general Z-continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates in an ...
متن کاملRational points near manifolds and metric Diophantine approximation
This work is motivated by problems on simultaneous Diophantine approximation on manifolds, namely, establishing Khintchine and Jarńık type theorems for submanifolds of Rn. These problems have attracted a lot of interest since Kleinbock and Margulis proved a related conjecture of Alan Baker and V.G. Sprindžuk. They have been settled for planar curves but remain open in higher dimensions. In this...
متن کاملRational Points on Singular Intersections of Quadrics
— Given an intersection of two quadrics X ⊂ Pm−1, with m > 9, the quantitative arithmetic of the set X(Q) is investigated under the assumption that the singular locus of X consists of a pair of conjugate singular points defined over Q(i).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2005
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-005-0683-x